From 0bdf81d0add819d6df102937c37b460c52fd1790 Mon Sep 17 00:00:00 2001 From: Rob Hyndman Date: Fri, 22 Mar 2024 10:57:09 +1100 Subject: [PATCH 1/2] Added R code from seminar --- .../assignments/Project/execute-results/html.json | 8 +++++--- _freeze/week4/index/execute-results/html.json | 8 +++++--- week4/index.qmd | 13 ++++++++++++- 3 files changed, 22 insertions(+), 7 deletions(-) diff --git a/_freeze/assignments/Project/execute-results/html.json b/_freeze/assignments/Project/execute-results/html.json index 3f86103..70de0fe 100644 --- a/_freeze/assignments/Project/execute-results/html.json +++ b/_freeze/assignments/Project/execute-results/html.json @@ -1,9 +1,11 @@ { - "hash": "2aa3f53c5859287b5f470c76577c5aa8", + "hash": "18fb10569fdba3545f925be2b27d438c", "result": { "engine": "knitr", - "markdown": "---\ntitle: Retail Project\n---\n\n\n\n\n**Objective:** To forecast a real time series using ETS and ARIMA models.\n\n**Data:** Each student will be use a different time series, selected using their student ID number as follows. This is the same series that you used in [Assignment 2](A2.qmd).\n\n```r\nlibrary(fpp3)\nget_my_data <- function(student_id) {\n set.seed(student_id)\n all_data <- readr::read_rds(\"https://bit.ly/monashretaildata\")\n while(TRUE) {\n retail <- filter(all_data, `Series ID` == sample(`Series ID`, 1)) \n if(!any(is.na(fill_gaps(retail)$Turnover))) return(retail)\n }\n}\n# Replace the argument with your student ID\nretail <- get_my_data(12345678)\n```\n\n**Assignment value:** This assignment is worth 20% of the overall unit assessment.\n\n**Report:**\n\nYou should produce forecasts of the series using ETS and ARIMA models. Write a report in Rmarkdown or Quarto format of your analysis explaining carefully what you have done and why you have done it. Your report should include the following elements.\n\n* A discussion of the statistical features of the original data, including the effect of COVID-19 on your series. [4 marks]\n* Explanation of transformations and differencing used. You should use a unit-root test as part of the discussion. [5 marks]\n* A description of the methodology used to create a short-list of appropriate ARIMA models and ETS models. Include discussion of AIC values as well as results from applying the models to a test-set consisting of the last 24 months of the data provided. [6 marks]\n* Choose one ARIMA model and one ETS model based on this analysis and show parameter estimates, residual diagnostics, forecasts and prediction intervals for both models. Diagnostic checking for both models should include ACF graphs and the Ljung-Box test. [8 marks]\n* Comparison of the results from each of your preferred models. Which method do you think gives the better forecasts? Explain with reference to the test-set. [2 marks]\n* Apply your two chosen models to the full data set, re-estimating the parameters but not changing the model structure. Produce out-of-sample point forecasts and 80% prediction intervals for each model for two years past the end of the data provided. [4 marks]\n* Obtain up-to-date data from the [ABS website](https://www.abs.gov.au/statistics/industry/retail-and-wholesale-trade/retail-trade-australia) (Table 11). You may need to use the previous release of data, rather than the latest release. Compare your forecasts with the actual numbers. How well did you do? [5 marks]\n* A discussion of benefits and limitations of the models for your data. [3 marks]\n* Graphs should be properly labelled, including appropriate units of measurement. [3 marks]\n\n**Notes**\n\n* Your submission must include the Rmarkdown or Quarto file (.Rmd or .qmd), and should run without error.\n* There will be a 5 marks penalty if file does not run without error.\n* You may also include a knitted version of the document (HTML preferred), but it is not required.\n* When using the updated ABS data set, do not edit the downloaded file in any way.\n* There is no need to provide the updated ABS data with your submission.\n\n\n\n\n


Due: 24 May 2024
  Submit  
\n", - "supporting": [], + "markdown": "---\ntitle: Retail Project\n---\n\n\n\n\n**Objective:** To forecast a real time series using ETS and ARIMA models.\n\n**Data:** The data are monthly measures of retail trade volume in Australia, [obtained from the ABS](https://www.abs.gov.au/methodologies/retail-trade-australia-methodology/jan-2024). Each student will be use a different time series, selected using their student ID number as follows. This is the same series that you used in [Assignment 2](A2.qmd).\n\n```r\nlibrary(fpp3)\nget_my_data <- function(student_id) {\n set.seed(student_id)\n all_data <- readr::read_rds(\"https://bit.ly/monashretaildata\")\n while(TRUE) {\n retail <- filter(all_data, `Series ID` == sample(`Series ID`, 1))\n if(!any(is.na(fill_gaps(retail)$Turnover))) return(retail)\n }\n}\n# Replace the argument with your student ID\nretail <- get_my_data(12345678)\n```\n\n**Assignment value:** This assignment is worth 20% of the overall unit assessment.\n\n**Report:**\n\nYou should produce forecasts of the series using ETS and ARIMA models. Write a report in Rmarkdown or Quarto format of your analysis explaining carefully what you have done and why you have done it. Your report should include the following elements.\n\n* A discussion of the statistical features of the original data, including the effect of COVID-19 on your series. [4 marks]\n* Explanation of transformations and differencing used. You should use a unit-root test as part of the discussion. [5 marks]\n* A description of the methodology used to create a short-list of appropriate ARIMA models and ETS models. Include discussion of AIC values as well as results from applying the models to a test-set consisting of the last 24 months of the data provided. [6 marks]\n* Choose one ARIMA model and one ETS model based on this analysis and show parameter estimates, residual diagnostics, forecasts and prediction intervals for both models. Diagnostic checking for both models should include ACF graphs and the Ljung-Box test. [8 marks]\n* Comparison of the results from each of your preferred models. Which method do you think gives the better forecasts? Explain with reference to the test-set. [2 marks]\n* Apply your two chosen models to the full data set, re-estimating the parameters but not changing the model structure. Produce out-of-sample point forecasts and 80% prediction intervals for each model for two years past the end of the data provided. [4 marks]\n* Obtain up-to-date data from the [ABS website](https://www.abs.gov.au/statistics/industry/retail-and-wholesale-trade/retail-trade-australia) (Table 11). You may need to use the previous release of data, rather than the latest release. Compare your forecasts with the actual numbers. How well did you do? [5 marks]\n* A discussion of benefits and limitations of the models for your data. [3 marks]\n* Graphs should be properly labelled, including appropriate units of measurement. [3 marks]\n\n**Notes**\n\n* Your submission must include the Rmarkdown or Quarto file (.Rmd or .qmd), and should run without error.\n* There will be a 5 marks penalty if file does not run without error.\n* You may also include a knitted version of the document (HTML preferred), but it is not required.\n* When using the updated ABS data set, do not edit the downloaded file in any way.\n* There is no need to provide the updated ABS data with your submission.\n\n\n\n\n


Due: 24 May 2024
  Submit  
\n", + "supporting": [ + "Project_files" + ], "filters": [ "rmarkdown/pagebreak.lua" ], diff --git a/_freeze/week4/index/execute-results/html.json b/_freeze/week4/index/execute-results/html.json index 09b8638..b01a4ff 100644 --- a/_freeze/week4/index/execute-results/html.json +++ b/_freeze/week4/index/execute-results/html.json @@ -1,9 +1,11 @@ { - "hash": "e7f94273921daac99cfd07d9d41f4c79", + "hash": "efcc5dbd8e02afc4aaabc093afdacc88", "result": { "engine": "knitr", - "markdown": "---\ntitle: \"Week 4: The forecaster's toolbox\"\n---\n\n::: {.cell}\n\n:::\n\n\n\n## What you will learn this week\n\n* Four benchmark forecasting methods that we will use for comparison\n* Fitted values, residuals\n* Forecasting with transformations\n\n## Pre-class activities\n\nRead [Chapter 5 of the textbook](https://otexts.com/fpp3/toolbox.html) and watch all embedded videos\n\n## Exercises (on your own or in tutorial)\n\nComplete Exercises 1-5, 9-10 from [Section 3.7 of the book](https://otexts.com/fpp3/decomposition-exercises.html).\n\n\n\n## Slides for seminar\n\n\nDownload pdf\n\n## Seminar activities\n\n1. Create a training set for household wealth (`hh_budget`) by withholding the last four years as a test set.\n2. Fit all the appropriate benchmark methods to the training set and forecast the periods covered by the test set.\n3. Compute the accuracy of your forecasts. Which method does best?\n4. Do the residuals from the best method resemble white noise?\n\n\n\n## Assignments\n\n* [Assignment 2](../assignments/A2.qmd) is due on Sunday 24 March.\n* [Assignment 3](../assignments/A3.qmd) is due on Friday 12 April.\n", - "supporting": [], + "markdown": "---\ntitle: \"Week 4: The forecaster's toolbox\"\n---\n\n::: {.cell}\n\n:::\n\n\n\n\n## What you will learn this week\n\n* Four benchmark forecasting methods that we will use for comparison\n* Fitted values, residuals\n* Forecasting with transformations\n\n## Pre-class activities\n\nRead [Chapter 5 of the textbook](https://otexts.com/fpp3/toolbox.html) and watch all embedded videos\n\n## Exercises (on your own or in tutorial)\n\nComplete Exercises 1-5, 9-10 from [Section 3.7 of the book](https://otexts.com/fpp3/decomposition-exercises.html).\n\n\n\n\n## Slides for seminar\n\n\nDownload pdf\n\n\n\n\n[**R code used in seminar**](seminar_code.R)\n\n## Seminar activities\n\n\n\n\n\n1. Create a training set for household wealth (`hh_budget`) by withholding the last four years as a test set.\n2. Fit all the appropriate benchmark methods to the training set and forecast the periods covered by the test set.\n3. Compute the accuracy of your forecasts. Which method does best?\n4. Do the residuals from the best method resemble white noise?\n\n::: {.cell}\n::: {.cell-output .cell-output-stdout}\n\n```\n\n\n## Assignments\n\n* [Assignment 2](../assignments/A2.qmd) is due on Sunday 24 March.\n* [Assignment 3](../assignments/A3.qmd) is due on Friday 12 April.\n```\n\n\n:::\n:::\n", + "supporting": [ + "index_files" + ], "filters": [ "rmarkdown/pagebreak.lua" ], diff --git a/week4/index.qmd b/week4/index.qmd index 788be0e..0b4b3a5 100644 --- a/week4/index.qmd +++ b/week4/index.qmd @@ -24,6 +24,17 @@ Complete Exercises 1-5, 9-10 from [Section 3.7 of the book](https://otexts.com/f ```{r} #| output: asis show_slides(week) -show_activity(week) +``` + +[**R code used in seminar**](seminar_code.R) + +## Seminar activities + +```{r} +#| child: activities.md +``` + + +```{r} show_assignments(week) ``` From cdd234e92715f151359c0da7be0dc93246335c6d Mon Sep 17 00:00:00 2001 From: Rob Hyndman Date: Fri, 22 Mar 2024 14:18:27 +1100 Subject: [PATCH 2/2] Added ex solutions for week 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.cell-code}\nlibrary(fpp3)\n```\n:::\n\n\n\n# fpp3 2.10, Ex 6\n\n> The `aus_arrivals` data set comprises quarterly international arrivals (in thousands) to Australia from Japan, New Zealand, UK and the US. Use `autoplot()`, `gg_season()` and `gg_subseries()` to compare the differences between the arrivals from these four countries. Can you identify any unusual observations?\n\n\n\n::: {.cell}\n\n```{.r .cell-code}\naus_arrivals |> autoplot(Arrivals) +\n labs(title=\"Quarterly international arrivals to Australia\",\n y=\"Visitors ('000)\")\n```\n\n::: {.cell-output-display}\n![](ex3-sol_files/figure-html/unnamed-chunk-2-1.png){width=672}\n:::\n:::\n\n\n\nGenerally the number of arrivals to Australia is increasing over the entire series, with the exception of Japanese visitors which begin to decline after 1995. The series appear to have a seasonal pattern which varies proportionately to the number of arrivals. Interestingly, the number of visitors from NZ peaks sharply in 1988. The seasonal pattern from Japan appears to change substantially.\n\n\n\n::: {.cell}\n\n```{.r .cell-code}\naus_arrivals |> gg_season(Arrivals, labels = \"both\")\n```\n\n::: {.cell-output-display}\n![](ex3-sol_files/figure-html/unnamed-chunk-3-1.png){width=672}\n:::\n:::\n\n\n\nThe seasonal pattern of arrivals appears to vary between each country. In particular, arrivals from the UK appears to be lowest in Q2 and Q3, and increase substantially for Q4 and Q1. Whereas for NZ visitors, the lowest period of arrivals is in Q1, and highest in Q3. Similar variations can be seen for Japan and US.\n\n\n\n::: {.cell}\n\n```{.r .cell-code}\naus_arrivals |> gg_subseries(Arrivals)\n```\n\n::: {.cell-output-display}\n![](ex3-sol_files/figure-html/unnamed-chunk-4-1.png){width=672}\n:::\n:::\n\n\n\nThe subseries plot reveals more interesting features. It is evident that whilst the UK arrivals is increasing, most of this increase is seasonal. More arrivals are coming during Q1 and Q4, whilst the increase in Q2 and Q3 is less extreme. The growth in arrivals from NZ and US appears fairly similar across all quarters. There exists an unusual spike in arrivals from the US in 1992 Q3.\n\nUnusual observations:\n\n - 2000 Q3: Spikes from the US (Sydney Olympics arrivals)\n - 2001 Q3-Q4 are unusual for US (9/11 effect)\n - 1991 Q3 is unusual for the US (Gulf war effect?)\n\n# fpp3 2.10, Ex 7\n\n> Monthly Australian retail data is provided in aus_retail. Select one of the time series as follows (but choose your own seed value):\n>\n> ```r\n> set.seed(12345678)\n> myseries <- aus_retail |>\n> filter(`Series ID` == sample(aus_retail$`Series ID`,1))\n> ```\n>\n> Explore your chosen retail time series using the following functions:\n>\n> ```r\n> autoplot(), gg_season(), gg_subseries(), gg_lag(), ACF() |> autoplot()\n> ```\n\n\n\n::: {.cell}\n\n```{.r .cell-code}\nset.seed(12345678)\nmyseries <- aus_retail |>\n filter(`Series ID` == sample(aus_retail$`Series ID`,1))\nmyseries |>\n autoplot(Turnover) +\n labs(y = \"Turnover (million $AUD)\", x = \"Time (Years)\",\n title = myseries$Industry[1],\n subtitle = myseries$State[1])\n```\n\n::: {.cell-output-display}\n![](ex3-sol_files/figure-html/ex6-1.png){width=672}\n:::\n:::\n\n\n\nThe data features a non-linear upward trend and a strong seasonal pattern. The variability in the data appears proportional to the amount of turnover (level of the series) over the time period.\n\n\n\n::: {.cell}\n\n```{.r .cell-code}\nmyseries |>\n gg_season(Turnover, labels = \"both\") +\n labs(y = \"Turnover (million $AUD)\",\n title = myseries$Industry[1],\n subtitle = myseries$State[1])\n```\n\n::: {.cell-output-display}\n![](ex3-sol_files/figure-html/unnamed-chunk-5-1.png){width=672}\n:::\n:::\n\n\n\nStrong seasonality is evident in the season plot. Large increases in clothing retailing can be observed in December (probably a Christmas effect). There is also a peak in July that appears to be getting stronger over time. 2016 had an unusual pattern in the first half of the year.\n\n\n\n::: {.cell}\n\n```{.r .cell-code}\nmyseries |>\n gg_subseries(Turnover) +\n labs(y = \"Turnover (million $AUD)\", x=\"\")\n```\n\n::: {.cell-output-display}\n![](ex3-sol_files/figure-html/unnamed-chunk-6-1.png){width=672}\n:::\n:::\n\n\n\nThere is a strong trend in all months, with the largest trend in December and a larger increase in July and August than most other months.\n\n\n\n::: {.cell}\n\n```{.r .cell-code}\nmyseries |>\n gg_lag(Turnover, lags=1:24, geom='point') + facet_wrap(~ .lag, ncol=6)\n```\n\n::: {.cell-output-display}\n![](ex3-sol_files/figure-html/unnamed-chunk-7-1.png){width=672}\n:::\n\n```{.r .cell-code}\nmyseries |>\n ACF(Turnover, lag_max = 50) |>\n autoplot()\n```\n\n::: {.cell-output-display}\n![](ex3-sol_files/figure-html/unnamed-chunk-7-2.png){width=672}\n:::\n:::\n\n\n\n# fpp3 2.10, Ex 8\n\n> Use the following graphics functions: `autoplot()`, `gg_season()`, `gg_subseries()`, `gg_lag()`, `ACF()` and explore features from the following time series: \"Total Private\" `Employed` from `us_employment`, `Bricks` from `aus_production`, `Hare` from `pelt`, \"H02\" `Cost` from `PBS`, and `us_gasoline`.\n>\n> + Can you spot any seasonality, cyclicity and trend?\n> + What do you learn about the series?\n> + What can you say about the seasonal patterns?\n> + Can you identify any unusual years?\n\n## Total Private Employment in the US\n\n\n\n::: {.cell}\n\n```{.r .cell-code}\nus_employment |>\n filter(Title == \"Total Private\") |>\n autoplot(Employed)\n```\n\n::: {.cell-output-display}\n![](ex3-sol_files/figure-html/unnamed-chunk-8-1.png){width=672}\n:::\n:::\n\n\n\nThere is a strong trend and seasonality. Some cyclic behaviour is seen, with a big drop due to the global financial crisis.\n\n\n\n::: {.cell}\n\n```{.r .cell-code}\nus_employment |>\n filter(Title == \"Total Private\") |>\n gg_season(Employed)\n```\n\n::: {.cell-output-display}\n![](ex3-sol_files/figure-html/unnamed-chunk-9-1.png){width=672}\n:::\n:::\n\n::: {.cell}\n\n```{.r .cell-code}\nus_employment |>\n filter(Title == \"Total Private\") |>\n gg_subseries(Employed)\n```\n\n::: {.cell-output-display}\n![](ex3-sol_files/figure-html/unnamed-chunk-10-1.png){width=672}\n:::\n:::\n\n::: {.cell}\n\n```{.r .cell-code}\nus_employment |>\n filter(Title == \"Total Private\") |>\n gg_lag(Employed)\n```\n\n::: {.cell-output-display}\n![](ex3-sol_files/figure-html/unnamed-chunk-11-1.png){width=672}\n:::\n:::\n\n::: {.cell}\n\n```{.r .cell-code}\nus_employment |>\n filter(Title == \"Total Private\") |>\n ACF(Employed) |>\n autoplot()\n```\n\n::: {.cell-output-display}\n![](ex3-sol_files/figure-html/unnamed-chunk-12-1.png){width=672}\n:::\n:::\n\n\n\nIn all of these plots, the trend is so dominant that it is hard to see anything else. We need to remove the trend so we can explore the other features of the data.\n\n## Brick production in Australia\n\n\n\n::: {.cell}\n\n```{.r .cell-code}\naus_production |>\n autoplot(Bricks)\n```\n\n::: {.cell-output-display}\n![](ex3-sol_files/figure-html/unnamed-chunk-13-1.png){width=672}\n:::\n:::\n\n\n\nA positive trend in the first 20 years, and a negative trend in the next 25 years. Strong quarterly seasonality, with some cyclicity -- note the recessions in the 1970s and 1980s.\n\n\n\n::: {.cell}\n\n```{.r .cell-code}\naus_production |>\n gg_season(Bricks)\n```\n\n::: {.cell-output-display}\n![](ex3-sol_files/figure-html/unnamed-chunk-14-1.png){width=672}\n:::\n:::\n\n\n\nBrick production tends to be lowest in the first quarter and peak in either quarter 2 or quarter 3.\n\n\n\n::: {.cell}\n\n```{.r .cell-code}\naus_production |>\n gg_subseries(Bricks)\n```\n\n::: {.cell-output-display}\n![](ex3-sol_files/figure-html/unnamed-chunk-15-1.png){width=672}\n:::\n:::\n\n\n\nThe decrease in the last 25 years has been weakest in Q1.\n\n\n\n::: {.cell}\n\n```{.r .cell-code}\naus_production |>\n gg_lag(Bricks, geom='point')\n```\n\n::: {.cell-output-display}\n![](ex3-sol_files/figure-html/unnamed-chunk-16-1.png){width=672}\n:::\n\n```{.r .cell-code}\naus_production |>\n ACF(Bricks) |> autoplot()\n```\n\n::: {.cell-output-display}\n![](ex3-sol_files/figure-html/unnamed-chunk-16-2.png){width=672}\n:::\n:::\n\n\n\nThe seasonality shows up as peaks at lags 4, 8, 12, 16, 20, .... The trend is seen with the slow decline on the positive side.\n\n## Snow hare trappings in Canada\n\n\n\n::: {.cell}\n\n```{.r .cell-code}\npelt |>\n autoplot(Hare)\n```\n\n::: {.cell-output-display}\n![](ex3-sol_files/figure-html/unnamed-chunk-17-1.png){width=672}\n:::\n:::\n\n\n\nThere is some cyclic behaviour with substantial variation in the length of the period.\n\n\n\n::: {.cell}\n\n```{.r .cell-code}\npelt |>\n gg_lag(Hare, geom='point')\n```\n\n::: {.cell-output-display}\n![](ex3-sol_files/figure-html/unnamed-chunk-18-1.png){width=672}\n:::\n\n```{.r .cell-code}\npelt |>\n ACF(Hare) |> autoplot()\n```\n\n::: {.cell-output-display}\n![](ex3-sol_files/figure-html/unnamed-chunk-18-2.png){width=672}\n:::\n:::\n\n\n\nThe cyclic period seems to have an average of about 10 (due to the local maximum in ACF at lag 10).\n\n## H02 sales in Australia\n\nThere are four series corresponding to H02 sales, so we will add them together.\n\n\n\n::: {.cell}\n\n```{.r .cell-code}\nh02 <- PBS |>\n filter(ATC2 == \"H02\") |>\n group_by(ATC2) |>\n summarise(Cost = sum(Cost)) |>\n ungroup()\n```\n:::\n::: {.cell}\n\n```{.r .cell-code}\nh02 |>\n autoplot(Cost)\n```\n\n::: {.cell-output-display}\n![](ex3-sol_files/figure-html/unnamed-chunk-20-1.png){width=672}\n:::\n:::\n\n\n\nA positive trend with strong monthly seasonality, dropping suddenly every February.\n\n\n\n::: {.cell}\n\n```{.r .cell-code}\nh02 |>\n gg_season(Cost)\n```\n\n::: {.cell-output-display}\n![](ex3-sol_files/figure-html/unnamed-chunk-21-1.png){width=672}\n:::\n:::\n\n::: {.cell}\n\n```{.r .cell-code}\nh02 |>\n gg_subseries(Cost)\n```\n\n::: {.cell-output-display}\n![](ex3-sol_files/figure-html/unnamed-chunk-22-1.png){width=672}\n:::\n:::\n\n\n\nThe trends have been greater in the higher peaking months -- this leads to increasing seasonal variation.\n\n\n\n::: {.cell}\n\n```{.r .cell-code}\nh02 |>\n gg_lag(Cost, geom='point', lags=1:16)\n```\n\n::: {.cell-output-display}\n![](ex3-sol_files/figure-html/unnamed-chunk-23-1.png){width=672}\n:::\n\n```{.r .cell-code}\nh02 |>\n ACF(Cost) |> autoplot()\n```\n\n::: {.cell-output-display}\n![](ex3-sol_files/figure-html/unnamed-chunk-23-2.png){width=672}\n:::\n:::\n\n\n\nThe large January sales show up as a separate cluster of points in the lag plots. The strong seasonality is clear in the ACF plot.\n\n## US gasoline sales\n\n\n\n::: {.cell}\n\n```{.r .cell-code}\nus_gasoline |>\n autoplot(Barrels)\n```\n\n::: {.cell-output-display}\n![](ex3-sol_files/figure-html/unnamed-chunk-24-1.png){width=672}\n:::\n:::\n\n\n\nA positive trend until 2008, and then the global financial crisis led to a drop in sales until 2012. The shape of the seasonality seems to have changed over time.\n\n\n\n::: {.cell}\n\n```{.r .cell-code}\nus_gasoline |>\n gg_season(Barrels)\n```\n\n::: {.cell-output-display}\n![](ex3-sol_files/figure-html/unnamed-chunk-25-1.png){width=672}\n:::\n:::\n\n\n\nThere is a lot of noise making it hard to see the overall seasonal pattern. However, it seems to drop towards the end of quarter 4.\n\n\n\n::: {.cell}\n\n```{.r .cell-code}\nus_gasoline |>\n gg_subseries(Barrels)\n```\n\n::: {.cell-output-display}\n![](ex3-sol_files/figure-html/unnamed-chunk-26-1.png){width=672}\n:::\n:::\n\n\n\nThe blue lines are helpful in seeing the average seasonal pattern.\n\n\n\n::: {.cell}\n\n```{.r .cell-code}\nus_gasoline |>\n gg_lag(Barrels, geom='point', lags=1:16)\n```\n\n::: {.cell-output-display}\n![](ex3-sol_files/figure-html/unnamed-chunk-27-1.png){width=672}\n:::\n\n```{.r .cell-code}\nus_gasoline |>\n ACF(Barrels, lag_max = 150) |> autoplot()\n```\n\n::: {.cell-output-display}\n![](ex3-sol_files/figure-html/unnamed-chunk-27-2.png){width=672}\n:::\n:::\n\n\n\nThe seasonality is seen if we increase the lags to at least 2 years (approx 104 weeks)\n\n# fpp3 2.10, Ex 9\n\n> The following time plots and ACF plots correspond to four different time series. Your task is to match each time plot in the first row with one of the ACF plots in the second row.\n\n\n\n::: {.cell}\n::: {.cell-output-display}\n![](ex3-sol_files/figure-html/acfguess-1.png){width=1152}\n:::\n:::\n\n\n\n1-B, 2-A, 3-D, 4-C\n\n# fpp3 2.10, Ex 10\n\n> The `aus_livestock` data contains the monthly total number of pigs slaughtered in Victoria, Australia, from Jul 1972 to Dec 2018. Use `filter()` to extract pig slaughters in Victoria between 1990 and 1995. Use `autoplot` and `ACF` for this data. How do they differ from white noise? If a longer period of data is used, what difference does it make to the ACF?\n\n\n\n::: {.cell}\n\n```{.r .cell-code}\nvic_pigs <- aus_livestock |>\n filter(Animal == \"Pigs\", State == \"Victoria\", between(year(Month), 1990, 1995))\nvic_pigs\n```\n\n::: {.cell-output .cell-output-stdout}\n\n```\n# A tsibble: 72 x 4 [1M]\n# Key: Animal, State [1]\n Month Animal State Count\n \n 1 1990 Jan Pigs Victoria 76000\n 2 1990 Feb Pigs Victoria 78100\n 3 1990 Mar Pigs Victoria 77600\n 4 1990 Apr Pigs Victoria 84100\n 5 1990 May Pigs Victoria 98000\n 6 1990 Jun Pigs Victoria 89100\n 7 1990 Jul Pigs Victoria 93500\n 8 1990 Aug Pigs Victoria 84700\n 9 1990 Sep Pigs Victoria 74500\n10 1990 Oct Pigs Victoria 91900\n# ℹ 62 more rows\n```\n\n\n:::\n:::\n\n::: {.cell}\n\n```{.r .cell-code}\nvic_pigs |>\n autoplot(Count)\n```\n\n::: {.cell-output-display}\n![](ex3-sol_files/figure-html/unnamed-chunk-30-1.png){width=672}\n:::\n:::\n\n\n\nAlthough the values appear to vary erratically between months, a general upward trend is evident between 1990 and 1995. In contrast, a white noise plot does not exhibit any trend.\n\n\n\n::: {.cell}\n\n```{.r .cell-code}\nvic_pigs |> ACF(Count) |> autoplot()\n```\n\n::: {.cell-output-display}\n![](ex3-sol_files/figure-html/unnamed-chunk-31-1.png){width=672}\n:::\n:::\n\n\n\nThe first 14 lags are significant, as the ACF slowly decays. This suggests that the data contains a trend. A white noise ACF plot would not usually contain any significant lags. The large spike at lag 12 suggests there is some seasonality in the data.\n\n\n\n::: {.cell}\n\n```{.r .cell-code}\naus_livestock |>\n filter(Animal == \"Pigs\", State == \"Victoria\") |>\n ACF(Count) |>\n autoplot()\n```\n\n::: {.cell-output-display}\n![](ex3-sol_files/figure-html/unnamed-chunk-32-1.png){width=672}\n:::\n:::\n\n\n\nThe longer series has much larger autocorrelations, plus clear evidence of seasonality at the seasonal lags of $12, 24, \\dots$.\n\n# fpp3 2.10, Ex 11\n\n> a. Use the following code to compute the daily changes in Google closing stock prices.\n>\n> ```r\n> dgoog <- gafa_stock |>\n> filter(Symbol == \"GOOG\", year(Date) >= 2018) |>\n> mutate(trading_day = row_number()) |>\n> update_tsibble(index = trading_day, regular = TRUE) |>\n> mutate(diff = difference(Close))\n> ```\n>\n> b. Why was it necessary to re-index the tsibble?\n> c. Plot these differences and their ACF.\n> d. Do the changes in the stock prices look like white noise?\n\n\n\n::: {.cell}\n\n```{.r .cell-code}\ndgoog <- gafa_stock |>\n filter(Symbol == \"GOOG\", year(Date) >= 2018) |>\n mutate(trading_day = row_number()) |>\n update_tsibble(index = trading_day, regular = TRUE) |>\n mutate(diff = difference(Close))\n```\n:::\n\n\n\nThe tsibble needed re-indexing as trading happens irregularly. The new index is based only on trading days.\n\n\n\n::: {.cell}\n\n```{.r .cell-code}\ndgoog |> autoplot(diff)\n```\n\n::: {.cell-output-display}\n![](ex3-sol_files/figure-html/unnamed-chunk-34-1.png){width=672}\n:::\n\n```{.r .cell-code}\ndgoog |> ACF(diff, lag_max=100) |> autoplot()\n```\n\n::: {.cell-output-display}\n![](ex3-sol_files/figure-html/unnamed-chunk-34-2.png){width=672}\n:::\n:::\n\n\n\nThere are some small significant autocorrelations out to lag 24, but nothing after that. 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Transforming data to remove some sources of variation\n* Decomposing a time series into trend-cycle, seasonal and remainder components\n* Seasonal adjustment\n\n## Pre-class activities\n\nRead [Chapter 3 of the textbook](https://otexts.com/fpp3/decomposition.html) and watch all embedded videos\n\n## Exercises (on your own or in tutorial)\n\nComplete Exercises 6-11 from [Section 2.10 of the book](https://otexts.com/fpp3/graphics-exercises.html).\n\n\n\n\n## Slides for seminar\n\n\nDownload pdf\n\n\n\n\n[**R code used in seminar**](seminar_code.R)\n\n## Seminar activities\n\n\n\n\n\n\n1. Produce an STL decomposition as follows\n\n ```r\n us_construction <- us_employment |>\n filter(Title == \"Construction\", year(Month) > 1980)\n dcmp <- us_construction |>\n model(stl = STL(Employed ~ trend(window = 9) + season(window = 11)))\n dcmp |> components() |> autoplot()\n ```\n2. What happens as you change the values of the two `window` arguments?\n3. How does the seasonal shape change over time? *[Hint: Try plotting the seasonal component using `gg_season`.]*\n4. Can you produce a plausible seasonally adjusted series? *[Hint: `season_adjust` is returned by `components()`.]*\n\n\n## Assignments\n\n* [Assignment 2](../assignments/A2.qmd) is due on Sunday 24 March.\n", - "supporting": [], + "markdown": "---\ntitle: \"Week 3: Time series decomposition\"\n---\n\n::: {.cell}\n\n:::\n\n\n\n\n\n## What you will learn this week\n\n* Transforming data to remove some sources of variation\n* Decomposing a time series into trend-cycle, seasonal and remainder components\n* Seasonal adjustment\n\n## Pre-class activities\n\nRead [Chapter 3 of the textbook](https://otexts.com/fpp3/decomposition.html) and watch all embedded videos\n\n## Exercises (on your own or in tutorial)\n\nComplete Exercises 6-11 from [Section 2.10 of the book](https://otexts.com/fpp3/graphics-exercises.html).\n\n[**Solutions to Exercises**](ex3-sol.qmd)\n\n\n\n\n\n## Slides for seminar\n\n\nDownload pdf\n\n\n\n\n\n[**R code used in seminar**](seminar_code.R)\n\n## Seminar activities\n\n\n\n\n\n\n\n1. Produce an STL decomposition as follows\n\n ```r\n us_construction <- us_employment |>\n filter(Title == \"Construction\", year(Month) > 1980)\n dcmp <- us_construction |>\n model(stl = STL(Employed ~ trend(window = 9) + season(window = 11)))\n dcmp |> components() |> autoplot()\n ```\n2. What happens as you change the values of the two `window` arguments?\n3. How does the seasonal shape change over time? *[Hint: Try plotting the seasonal component using `gg_season`.]*\n4. Can you produce a plausible seasonally adjusted series? *[Hint: `season_adjust` is returned by `components()`.]*\n\n\n## Assignments\n\n* [Assignment 2](../assignments/A2.qmd) is due on Sunday 24 March.\n", + "supporting": [ + "index_files" + ], "filters": [ "rmarkdown/pagebreak.lua" ], diff --git a/week3/ex3-sol.qmd b/week3/ex3-sol.qmd new file mode 100644 index 0000000..d978082 --- /dev/null +++ b/week3/ex3-sol.qmd @@ -0,0 +1,378 @@ +--- +title: "Exercise Week 3: Solutions" +--- + +```{r setup, include=FALSE} +knitr::opts_chunk$set(echo = TRUE, cache=TRUE) +``` + +```{r, message = FALSE} +library(fpp3) +``` + +# fpp3 2.10, Ex 6 + +> The `aus_arrivals` data set comprises quarterly international arrivals (in thousands) to Australia from Japan, New Zealand, UK and the US. Use `autoplot()`, `gg_season()` and `gg_subseries()` to compare the differences between the arrivals from these four countries. Can you identify any unusual observations? + +```{r} +aus_arrivals |> autoplot(Arrivals) + + labs(title="Quarterly international arrivals to Australia", + y="Visitors ('000)") +``` + +Generally the number of arrivals to Australia is increasing over the entire series, with the exception of Japanese visitors which begin to decline after 1995. The series appear to have a seasonal pattern which varies proportionately to the number of arrivals. Interestingly, the number of visitors from NZ peaks sharply in 1988. The seasonal pattern from Japan appears to change substantially. + +```{r, fig.height=10} +aus_arrivals |> gg_season(Arrivals, labels = "both") +``` + +The seasonal pattern of arrivals appears to vary between each country. In particular, arrivals from the UK appears to be lowest in Q2 and Q3, and increase substantially for Q4 and Q1. Whereas for NZ visitors, the lowest period of arrivals is in Q1, and highest in Q3. Similar variations can be seen for Japan and US. + +```{r} +aus_arrivals |> gg_subseries(Arrivals) +``` + +The subseries plot reveals more interesting features. It is evident that whilst the UK arrivals is increasing, most of this increase is seasonal. More arrivals are coming during Q1 and Q4, whilst the increase in Q2 and Q3 is less extreme. The growth in arrivals from NZ and US appears fairly similar across all quarters. There exists an unusual spike in arrivals from the US in 1992 Q3. + +Unusual observations: + + - 2000 Q3: Spikes from the US (Sydney Olympics arrivals) + - 2001 Q3-Q4 are unusual for US (9/11 effect) + - 1991 Q3 is unusual for the US (Gulf war effect?) + +# fpp3 2.10, Ex 7 + +> Monthly Australian retail data is provided in aus_retail. Select one of the time series as follows (but choose your own seed value): +> +> ```r +> set.seed(12345678) +> myseries <- aus_retail |> +> filter(`Series ID` == sample(aus_retail$`Series ID`,1)) +> ``` +> +> Explore your chosen retail time series using the following functions: +> +> ```r +> autoplot(), gg_season(), gg_subseries(), gg_lag(), ACF() |> autoplot() +> ``` + +```{r ex6} +set.seed(12345678) +myseries <- aus_retail |> + filter(`Series ID` == sample(aus_retail$`Series ID`,1)) +myseries |> + autoplot(Turnover) + + labs(y = "Turnover (million $AUD)", x = "Time (Years)", + title = myseries$Industry[1], + subtitle = myseries$State[1]) +``` + +The data features a non-linear upward trend and a strong seasonal pattern. The variability in the data appears proportional to the amount of turnover (level of the series) over the time period. + +```{r, dependson='ex6'} +myseries |> + gg_season(Turnover, labels = "both") + + labs(y = "Turnover (million $AUD)", + title = myseries$Industry[1], + subtitle = myseries$State[1]) +``` + +Strong seasonality is evident in the season plot. Large increases in clothing retailing can be observed in December (probably a Christmas effect). There is also a peak in July that appears to be getting stronger over time. 2016 had an unusual pattern in the first half of the year. + +```{r, dependson='ex6'} +myseries |> + gg_subseries(Turnover) + + labs(y = "Turnover (million $AUD)", x="") +``` + +There is a strong trend in all months, with the largest trend in December and a larger increase in July and August than most other months. + +```{r, dependson='ex6'} +myseries |> + gg_lag(Turnover, lags=1:24, geom='point') + facet_wrap(~ .lag, ncol=6) +myseries |> + ACF(Turnover, lag_max = 50) |> + autoplot() +``` + +# fpp3 2.10, Ex 8 + +> Use the following graphics functions: `autoplot()`, `gg_season()`, `gg_subseries()`, `gg_lag()`, `ACF()` and explore features from the following time series: "Total Private" `Employed` from `us_employment`, `Bricks` from `aus_production`, `Hare` from `pelt`, "H02" `Cost` from `PBS`, and `us_gasoline`. +> +> + Can you spot any seasonality, cyclicity and trend? +> + What do you learn about the series? +> + What can you say about the seasonal patterns? +> + Can you identify any unusual years? + +## Total Private Employment in the US + +```{r} +us_employment |> + filter(Title == "Total Private") |> + autoplot(Employed) +``` + +There is a strong trend and seasonality. Some cyclic behaviour is seen, with a big drop due to the global financial crisis. + +```{r} +us_employment |> + filter(Title == "Total Private") |> + gg_season(Employed) +``` + +```{r} +us_employment |> + filter(Title == "Total Private") |> + gg_subseries(Employed) +``` + +```{r} +us_employment |> + filter(Title == "Total Private") |> + gg_lag(Employed) +``` + +```{r} +us_employment |> + filter(Title == "Total Private") |> + ACF(Employed) |> + autoplot() +``` + +In all of these plots, the trend is so dominant that it is hard to see anything else. We need to remove the trend so we can explore the other features of the data. + +## Brick production in Australia + +```{r} +aus_production |> + autoplot(Bricks) +``` + +A positive trend in the first 20 years, and a negative trend in the next 25 years. Strong quarterly seasonality, with some cyclicity -- note the recessions in the 1970s and 1980s. + +```{r} +aus_production |> + gg_season(Bricks) +``` + +Brick production tends to be lowest in the first quarter and peak in either quarter 2 or quarter 3. + +```{r} +aus_production |> + gg_subseries(Bricks) +``` + +The decrease in the last 25 years has been weakest in Q1. + +```{r} +aus_production |> + gg_lag(Bricks, geom='point') +aus_production |> + ACF(Bricks) |> autoplot() +``` + +The seasonality shows up as peaks at lags 4, 8, 12, 16, 20, .... The trend is seen with the slow decline on the positive side. + +## Snow hare trappings in Canada + +```{r} +pelt |> + autoplot(Hare) +``` + +There is some cyclic behaviour with substantial variation in the length of the period. + +```{r} +pelt |> + gg_lag(Hare, geom='point') +pelt |> + ACF(Hare) |> autoplot() +``` + +The cyclic period seems to have an average of about 10 (due to the local maximum in ACF at lag 10). + +## H02 sales in Australia + +There are four series corresponding to H02 sales, so we will add them together. + +```{r} +h02 <- PBS |> + filter(ATC2 == "H02") |> + group_by(ATC2) |> + summarise(Cost = sum(Cost)) |> + ungroup() + +```{r} +h02 |> + autoplot(Cost) +``` + +A positive trend with strong monthly seasonality, dropping suddenly every February. + +```{r} +h02 |> + gg_season(Cost) +``` + +```{r} +h02 |> + gg_subseries(Cost) +``` + +The trends have been greater in the higher peaking months -- this leads to increasing seasonal variation. + +```{r} +h02 |> + gg_lag(Cost, geom='point', lags=1:16) +h02 |> + ACF(Cost) |> autoplot() +``` + +The large January sales show up as a separate cluster of points in the lag plots. The strong seasonality is clear in the ACF plot. + +## US gasoline sales + +```{r} +us_gasoline |> + autoplot(Barrels) +``` + +A positive trend until 2008, and then the global financial crisis led to a drop in sales until 2012. The shape of the seasonality seems to have changed over time. + +```{r} +us_gasoline |> + gg_season(Barrels) +``` + +There is a lot of noise making it hard to see the overall seasonal pattern. However, it seems to drop towards the end of quarter 4. + +```{r} +us_gasoline |> + gg_subseries(Barrels) +``` + +The blue lines are helpful in seeing the average seasonal pattern. + +```{r} +us_gasoline |> + gg_lag(Barrels, geom='point', lags=1:16) +us_gasoline |> + ACF(Barrels, lag_max = 150) |> autoplot() +``` + +The seasonality is seen if we increase the lags to at least 2 years (approx 104 weeks) + +# fpp3 2.10, Ex 9 + +> The following time plots and ACF plots correspond to four different time series. Your task is to match each time plot in the first row with one of the ACF plots in the second row. + +```{r} +#| label: acfguess +#| fig-asp: 0.5 +#| fig-width: 12 +#| echo: false +#| message: false +#| warning: false +library(patchwork) +cowtemp <- as_tsibble(fma::cowtemp) +USAccDeaths <- as_tsibble(USAccDeaths) +AirPassengers <- as_tsibble(AirPassengers) +mink <- as_tsibble(fma::mink) +tp1 <- autoplot(cowtemp, value) + + labs(x = "", y = "chirps per minute", title = "1. Daily temperature of cow") +tp2 <- autoplot(USAccDeaths, value) + + labs(x = "", y = "thousands", title = "2. Monthly accidental deaths") +tp3 <- autoplot(AirPassengers, value) + + labs(x = "", y = "thousands", title = "3. Monthly air passengers") +tp4 <- autoplot(mink, value) + + labs(x = "", y = "thousands", title = "4. Annual mink trappings") +acfb <- ACF(cowtemp, value) |> + autoplot() + + labs(x = "", title = "B") + + ylim(-0.45, 1) +acfa <- ACF(USAccDeaths, value) |> + autoplot() + + labs(x = "", title = "A") + + ylim(-0.45, 1) +acfd <- ACF(AirPassengers, value) |> + autoplot() + + labs(x = "", title = "D") + + ylim(-0.45, 1) +acfc <- ACF(mink, value) |> + autoplot() + + labs(x = "", title = "C") + + ylim(-0.45, 1) +(tp1 / acfa) | (tp2 / acfb) | (tp3 / acfc) | (tp4 / acfd) +``` + +1-B, 2-A, 3-D, 4-C + +# fpp3 2.10, Ex 10 + +> The `aus_livestock` data contains the monthly total number of pigs slaughtered in Victoria, Australia, from Jul 1972 to Dec 2018. Use `filter()` to extract pig slaughters in Victoria between 1990 and 1995. Use `autoplot` and `ACF` for this data. How do they differ from white noise? If a longer period of data is used, what difference does it make to the ACF? + +```{r} +#| fig-height: 3 +vic_pigs <- aus_livestock |> + filter(Animal == "Pigs", State == "Victoria", between(year(Month), 1990, 1995)) +vic_pigs +``` + +```{r} +#| fig-height: 3 +vic_pigs |> + autoplot(Count) +``` + +Although the values appear to vary erratically between months, a general upward trend is evident between 1990 and 1995. In contrast, a white noise plot does not exhibit any trend. + +```{r} +#| fig-height: 3 +vic_pigs |> ACF(Count) |> autoplot() +``` + +The first 14 lags are significant, as the ACF slowly decays. This suggests that the data contains a trend. A white noise ACF plot would not usually contain any significant lags. The large spike at lag 12 suggests there is some seasonality in the data. + +```{r} +#| fig-height: 3 +aus_livestock |> + filter(Animal == "Pigs", State == "Victoria") |> + ACF(Count) |> + autoplot() +``` + +The longer series has much larger autocorrelations, plus clear evidence of seasonality at the seasonal lags of $12, 24, \dots$. + +# fpp3 2.10, Ex 11 + +> a. Use the following code to compute the daily changes in Google closing stock prices. +> +> ```r +> dgoog <- gafa_stock |> +> filter(Symbol == "GOOG", year(Date) >= 2018) |> +> mutate(trading_day = row_number()) |> +> update_tsibble(index = trading_day, regular = TRUE) |> +> mutate(diff = difference(Close)) +> ``` +> +> b. Why was it necessary to re-index the tsibble? +> c. Plot these differences and their ACF. +> d. Do the changes in the stock prices look like white noise? + +```{r} +dgoog <- gafa_stock |> + filter(Symbol == "GOOG", year(Date) >= 2018) |> + mutate(trading_day = row_number()) |> + update_tsibble(index = trading_day, regular = TRUE) |> + mutate(diff = difference(Close)) +``` + +The tsibble needed re-indexing as trading happens irregularly. The new index is based only on trading days. + +```{r} +#| fig-height: 3 +dgoog |> autoplot(diff) +dgoog |> ACF(diff, lag_max=100) |> autoplot() +``` + +There are some small significant autocorrelations out to lag 24, but nothing after that. Given the probability of a false positive is 5%, these look similar to white noise. diff --git a/week3/index.qmd b/week3/index.qmd index 18a2cd3..988fa72 100644 --- a/week3/index.qmd +++ b/week3/index.qmd @@ -21,6 +21,8 @@ Read [Chapter 3 of the textbook](https://otexts.com/fpp3/decomposition.html) and Complete Exercises 6-11 from [Section 2.10 of the book](https://otexts.com/fpp3/graphics-exercises.html). +[**Solutions to Exercises**](ex3-sol.qmd) + ```{r} #| output: asis show_slides(week)
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