Forecasting: Principles and Practice Chapter 5 Exercises
Neil Martin
2024-09-11
Produce forecasts for the following series using whichever of NAIVE(y), SNAIVE(y) or RW(y ~ drift()) is more appropriate in each case:
Australian Population (global_economy)
Bricks (aus_production)
NSW Lambs (aus_livestock)
Household wealth (hh_budget).
Australian takeaway food turnover (aus_retail).
global_economy |>
filter(Country == "Australia") |>
model(RW(Population ~ drift())) |>
forecast(h = 5) |>
autoplot(global_economy) +
labs(title = "Australia Population",
subtitle = "5 Year Population Forecast")
bricks <- aus_production |>
filter_index("1970 Q1" ~ "2004 Q4") |>
select(Bricks)
bricks## # A tsibble: 140 x 2 [1Q]
## Bricks Quarter
## <dbl> <qtr>
## 1 386 1970 Q1
## 2 428 1970 Q2
## 3 434 1970 Q3
## 4 417 1970 Q4
## 5 385 1971 Q1
## 6 433 1971 Q2
## 7 453 1971 Q3
## 8 436 1971 Q4
## 9 399 1972 Q1
## 10 461 1972 Q2
## # ℹ 130 more rowsbricks |>
model(SNAIVE(Bricks)) |>
forecast(h = 5) |>
autoplot(bricks) +
labs(title = "Bricks",
subtitle = "Future 5 Quarter Forecast")
aus_livestock |>
filter(State == "New South Wales", Animal == 'Lambs') |>
model(SNAIVE(Count)) |>
forecast(h = 24) |>
autoplot(aus_livestock) +
labs(title = "Lambs in New South Wales",
subtitle = "Dec 2018 - Dec 2020 Forecast")
hh_budget |>
model(RW(Wealth ~ drift())) |>
forecast(h = 5) |>
autoplot(hh_budget) +
labs(title = "Household Wealth",
subtitle = "5 Year Household Wealth Forecast")
aus_retail |>
filter(Industry == "Cafes, restaurants and takeaway food services") |>
model(RW(Turnover ~ drift())) |>
forecast( h = 24) |>
autoplot(aus_retail) +
labs(title = "Australian Takeaway Food Turnover",
subtitle = "Apr 1982 - Dec 2018, Forecasted until Dec 2021") +
facet_wrap(~State, scales = "free")
Use the Facebook stock price (data set gafa_stock) to do the following:
Produce a time plot of the series.
Produce forecasts using the drift method and plot them.
Show that the forecasts are identical to extending the line drawn between the first and last observations.
Try using some of the other benchmark functions to forecast the same data set. Which do you think is best? Why?
fb_stock <- gafa_stock |>
filter(Symbol == "FB") |>
mutate(trading_day = row_number()) |>
update_tsibble(index = trading_day, regular = TRUE)
fb_stock |> autoplot() +
labs(title = "FB Stock Open Price")## Plot variable not specified, automatically selected `.vars = Open`
fb_stock |>
model(RW(Open ~ drift())) |>
forecast(h = 63) |>
autoplot(fb_stock) +
labs(title = "FB Stock Open Price",
y = "USD($)")
fb_stock |>
model(RW(Open ~ drift())) |>
forecast(h = 63) |>
autoplot(fb_stock) +
labs(title = "FB Stock Open Price") +
geom_segment(aes(x = 1, y = 54.83, xend = 1258, yend = 134.45),
colour = "red", linetype = "dashed")## Warning in geom_segment(aes(x = 1, y = 54.83, xend = 1258, yend = 134.45), : All aesthetics have length 1, but the data has 1258 rows.
## ℹ Please consider using `annotate()` or provide this layer with data containing
## a single row.
fb_stock |>
model(Drift = NAIVE(Open ~ drift()),
Mean = MEAN(Open),
Naive = NAIVE(Open)) |>
forecast(h = 63) |>
autoplot(fb_stock, level = NULL) +
labs(title = "FB Stock Open Price",
y = "USD($)")
None of the additional benchmarks are particularly useful. However, if I had to pick one it would be the drift.
Apply a seasonal naïve method to the quarterly Australian beer production data from 1992. Check if the residuals look like white noise, and plot the forecasts. The following code will help.
# Extract data of interest
recent_production <- aus_production |>
filter(year(Quarter) >= 1992)
# Define and estimate a model
fit <- recent_production |> model(SNAIVE(Beer))
# Look at the residuals
fit |> gg_tsresiduals()## Warning: Removed 4 rows containing missing values or values outside the scale range
## (`geom_line()`).## Warning: Removed 4 rows containing missing values or values outside the scale range
## (`geom_point()`).## Warning: Removed 4 rows containing non-finite outside the scale range
## (`stat_bin()`).
# Look a some forecasts
fit |> forecast() |> autoplot(recent_production)
The residuals are not white noise. This can be concluded from the results from the ACF function demonstrating peaks in Q4.
Repeat the previous exercise using the Australian Exports series from global_economy and the Bricks series from aus_production. Use whichever of NAIVE() or SNAIVE() is more appropriate in each case
aus_exports <- global_economy |>
filter(Country == "Australia")
aus_exports## # A tsibble: 58 x 9 [1Y]
## # Key: Country [1]
## Country Code Year GDP Growth CPI Imports Exports Population
## <fct> <fct> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 Australia AUS 1960 18573188487. NA 7.96 14.1 13.0 10276477
## 2 Australia AUS 1961 19648336880. 2.49 8.14 15.0 12.4 10483000
## 3 Australia AUS 1962 19888005376. 1.30 8.12 12.6 13.9 10742000
## 4 Australia AUS 1963 21501847911. 6.21 8.17 13.8 13.0 10950000
## 5 Australia AUS 1964 23758539590. 6.98 8.40 13.8 14.9 11167000
## 6 Australia AUS 1965 25931235301. 5.98 8.69 15.3 13.2 11388000
## 7 Australia AUS 1966 27261731437. 2.38 8.98 15.1 12.9 11651000
## 8 Australia AUS 1967 30389741292. 6.30 9.29 13.9 12.9 11799000
## 9 Australia AUS 1968 32657632434. 5.10 9.52 14.5 12.3 12009000
## 10 Australia AUS 1969 36620002240. 7.04 9.83 13.3 12.0 12263000
## # ℹ 48 more rowsfit <- aus_exports |>
model(NAIVE(Exports))
fit |> gg_tsresiduals() +
ggtitle("Residual Plot for Australian Exports")## Warning: Removed 1 row containing missing values or values outside the scale range
## (`geom_line()`).## Warning: Removed 1 row containing missing values or values outside the scale range
## (`geom_point()`).## Warning: Removed 1 row containing non-finite outside the scale range
## (`stat_bin()`).
fit |> forecast() |> autoplot(aus_exports) +
ggtitle("Australian Exports")
fit <- bricks |>
model(SNAIVE(Bricks))
fit |> gg_tsresiduals() +
ggtitle("Residual Plot for Brick Production")## Warning: Removed 4 rows containing missing values or values outside the scale range
## (`geom_line()`).## Warning: Removed 4 rows containing missing values or values outside the scale range
## (`geom_point()`).## Warning: Removed 4 rows containing non-finite outside the scale range
## (`stat_bin()`).
fit |> forecast() |> autoplot(bricks) +
ggtitle("Australian Brick Production")
This data is not seasonal for the exports, therefore NAIVE is a better choice of model. For the Bricks data, the SNAIVE is better as this is broken down into quarters. The lag plot demonstrates clear seasonality with brick production increasing during Q4 and a reduction in production until the following quarter next year.
Produce forecasts for the 7 Victorian series in aus_livestock using SNAIVE(). Plot the resulting forecasts including the historical data. Is this a reasonable benchmark for these series?
aus_livestock |>
filter(State == "Victoria") |>
model(SNAIVE(Count ~ lag("2 years"))) |>
forecast(h = "2 years") %>%
autoplot(aus_livestock) +
labs(title = "Animals in Victoria") +
facet_wrap(~Animal, scales = "free")
Lambs and Calves may benefit from a trend model as overtime the number of calves has increased steadily and the number of lambs increased. For the rest, there is clear seasonal patterns within the data so a SNAIVE model is more suitable.
Are the following statements true or false? Explain your answer.
Good forecast methods should have normally distributed residuals.
Yes normally distributed residuals outlines that there is less of a chance of the data being white noise and the model being more accurate.
A model with small residuals will give good forecasts.
No, even though there is little difference between the forecast and the actual values, the pattern of the data might change.
The best measure of forecast accuracy is MAPE.
This is generally the most used metric.
If your model doesn’t forecast well, you should make it more complicated.
Nope, sometimes choosing a more simplistic model can provide better results.
Always choose the model with the best forecast accuracy as measured on the test set.
No, this can result in overfitting. Consider the metric the model has against the validation/testing set.
For your retail time series (from Exercise 7 in Section 2.10):
Create a training dataset consisting of observations before 2011 using
set.seed(12345678)
myseries <- aus_retail |>
filter(`Series ID` == sample(aus_retail$`Series ID`,1))
myseries_train <- myseries |>
filter(year(Month) < 2011)Check that your data have been split appropriately by producing the following plot.
autoplot(myseries, Turnover) +
autolayer(myseries_train, Turnover, colour = "red")
#### Fit a seasonal naïve model using SNAIVE() applied to your training
data (myseries_train).
fit <- myseries_train |>
model(SNAIVE(Turnover))Check the residuals.
fit |> gg_tsresiduals()## Warning: Removed 12 rows containing missing values or values outside the scale range
## (`geom_line()`).## Warning: Removed 12 rows containing missing values or values outside the scale range
## (`geom_point()`).## Warning: Removed 12 rows containing non-finite outside the scale range
## (`stat_bin()`).
#### Produce forecasts for the test data
fc <- fit |>
forecast(new_data = anti_join(myseries, myseries_train))## Joining with `by = join_by(State, Industry, `Series ID`, Month, Turnover)`fc |> autoplot(myseries)
Compare the accuracy of your forecasts against the actual values.
fit |> accuracy()## # A tibble: 1 × 12
## State Industry .model .type ME RMSE MAE MPE MAPE MASE RMSSE ACF1
## <chr> <chr> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 Norther… Clothin… SNAIV… Trai… 0.439 1.21 0.915 5.23 12.4 1 1 0.768fc |> accuracy(myseries)## # A tibble: 1 × 12
## .model State Industry .type ME RMSE MAE MPE MAPE MASE RMSSE ACF1
## <chr> <chr> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 SNAIVE(T… Nort… Clothin… Test 0.836 1.55 1.24 5.94 9.06 1.36 1.28 0.601Consider the number of pigs slaughtered in New South Wales (data set aus_livestock).
Produce some plots of the data in order to become familiar with it.
pigs <- aus_livestock |>
filter(Animal == "Pigs" & State == "New South Wales")
pigs## # A tsibble: 558 x 4 [1M]
## # Key: Animal, State [1]
## Month Animal State Count
## <mth> <fct> <fct> <dbl>
## 1 1972 Jul Pigs New South Wales 97400
## 2 1972 Aug Pigs New South Wales 114700
## 3 1972 Sep Pigs New South Wales 109900
## 4 1972 Oct Pigs New South Wales 108300
## 5 1972 Nov Pigs New South Wales 122200
## 6 1972 Dec Pigs New South Wales 106900
## 7 1973 Jan Pigs New South Wales 96600
## 8 1973 Feb Pigs New South Wales 96700
## 9 1973 Mar Pigs New South Wales 121200
## 10 1973 Apr Pigs New South Wales 99300
## # ℹ 548 more rowspigs |> autoplot()## Plot variable not specified, automatically selected `.vars = Count`
pigs |> gg_season()## Plot variable not specified, automatically selected `y = Count`
pigs |> gg_subseries()## Plot variable not specified, automatically selected `y = Count`
#### Create a training set of 486 observations, withholding a test set
of 72 observations (6 years).
pigs_train <- pigs |>
filter(year(Month) < 2014)
autoplot(pigs, Count) +
autolayer(pigs_train, Count, colour = "red")
Try using various benchmark methods to forecast the training set and compare the results on the test set. Which method did best?
pigs_fit <- pigs_train |>
model(SNAIVE(Count))
accuracy(pigs_fit)## # A tibble: 1 × 12
## Animal State .model .type ME RMSE MAE MPE MAPE MASE RMSSE ACF1
## <fct> <fct> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 Pigs New Sou… SNAIV… Trai… -848. 14385. 10482. -1.85 10.1 1 1 0.606pigs_fc <- pigs_fit |>
forecast(h = 12, level = NULL) |>
autoplot(pigs_train) +
labs(title = "Piggy Forecast")
pigs_fc
Due to the stucture of the time series index, seasonal will likely always perform better.
Check the residuals of your preferred method. Do they resemble white noise?
pigs_fit |> gg_tsresiduals() +
ggtitle("Residuals")## Warning: Removed 12 rows containing missing values or values outside the scale range
## (`geom_line()`).## Warning: Removed 12 rows containing missing values or values outside the scale range
## (`geom_point()`).## Warning: Removed 12 rows containing non-finite outside the scale range
## (`stat_bin()`).
No, there does not appear to be white noise as the residuals are consistent.
Create a training set for household wealth (hh_budget) by withholding the last four years as a test set.
hh_budget_train <- hh_budget |>
filter(Year <= 2010)
fit <- hh_budget_train |>
model(RW(Wealth ~ drift()))
accuracy(fit)## # A tibble: 4 × 11
## Country .model .type ME RMSE MAE MPE MAPE MASE RMSSE ACF1
## <chr> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 Australia RW(Wea… Trai… 0 23.0 14.9 -0.173 4.26 0.984 0.997 -0.136
## 2 Canada RW(Wea… Trai… 1.60e-14 24.2 19.5 -0.137 4.46 0.957 0.984 0.0828
## 3 Japan RW(Wea… Trai… 1.49e-14 17.0 12.2 0.0106 2.40 0.796 0.914 0.130
## 4 USA RW(Wea… Trai… 1.85e-14 32.8 26.9 -0.186 5.32 0.962 0.995 0.0907fc <- fit |>
forecast(h = 6, level=NULL) |>
autoplot(hh_budget_train)+
labs(title = "6 Year Household Wealth Forecast")
fc
#### Create a training set for Australian takeaway food turnover
(aus_retail) by withholding the last four years as a test set.
takeaway <- aus_retail |>
filter(Industry == "Cafes, restaurants and takeaway food services")
tw_train <- takeaway |>
filter(year(Month) <= 2014)Fit all the appropriate benchmark methods to the training set and forecast the periods covered by the test set.
fit <- takeaway |>
model(RW(Turnover ~ drift()))
fit## # A mable: 8 x 3
## # Key: State, Industry [8]
## State Industry RW(Turnover ~ drift(…¹
## <chr> <chr> <model>
## 1 Australian Capital Territory Cafes, restaurants and ta… <RW w/ drift>
## 2 New South Wales Cafes, restaurants and ta… <RW w/ drift>
## 3 Northern Territory Cafes, restaurants and ta… <RW w/ drift>
## 4 Queensland Cafes, restaurants and ta… <RW w/ drift>
## 5 South Australia Cafes, restaurants and ta… <RW w/ drift>
## 6 Tasmania Cafes, restaurants and ta… <RW w/ drift>
## 7 Victoria Cafes, restaurants and ta… <RW w/ drift>
## 8 Western Australia Cafes, restaurants and ta… <RW w/ drift>
## # ℹ abbreviated name: ¹`RW(Turnover ~ drift())`fit |>
forecast ( h = 48) |>
autoplot(takeaway) +
labs(title = "Australian Takeaway Food Turnover",
subtitle = "Apr 1982 - Dec 2018, Forecasted until Dec 2022") +
facet_wrap(~State, scales = "free")
#### We will use the Bricks data from aus_production (Australian
quarterly clay brick production 1956–2005) for this exercise.
Use an STL decomposition to calculate the trend-cycle and seasonal indices. (Experiment with having fixed or changing seasonality.)
bricks_additive <- bricks |>
model(classical_decomposition(Bricks, type = "additive")) |>
components() |>
autoplot() +
labs(title = "Classical additive decomposition of Australian brick production")
bricks_additive## Warning: Removed 2 rows containing missing values or values outside the scale range
## (`geom_line()`).
bricks_multi <- bricks |>
model(classical_decomposition(Bricks, type = "multiplicative")) |>
components() |>
autoplot() +
labs(title = "Classical multiplicative decomposition of Australian brick production")
bricks_multi## Warning: Removed 2 rows containing missing values or values outside the scale range
## (`geom_line()`).
bricks_stl <- bricks |>
model(STL(Bricks ~ season(window = 4), robust = TRUE)) |>
components() |>
autoplot() +
labs(title = "STL decomposition of Australian brick production")
bricks_stl
bricks_stl_per <- bricks |>
model(STL(Bricks ~ season(window = 'periodic'), robust = TRUE)) |>
components() |>
autoplot() +
labs(title = "Periodic STL decomposition of Australian brick production")
bricks_stl_per
Compute and plot the seasonally adjusted data.
bricks## # A tsibble: 140 x 2 [1Q]
## Bricks Quarter
## <dbl> <qtr>
## 1 386 1970 Q1
## 2 428 1970 Q2
## 3 434 1970 Q3
## 4 417 1970 Q4
## 5 385 1971 Q1
## 6 433 1971 Q2
## 7 453 1971 Q3
## 8 436 1971 Q4
## 9 399 1972 Q1
## 10 461 1972 Q2
## # ℹ 130 more rowsbricks_season <- bricks |>
model(stl = STL(Bricks))
brick_comp <- components(bricks_season)
brick_season_adjust <- bricks |>
autoplot(Bricks, color = "green") +
autolayer(components(bricks_season), season_adjust, color = "red") +
labs(title = "Seasonally adjusted Australian bricks data")
brick_season_adjust
Use a naïve method to produce forecasts of the seasonally adjusted data.
brick_trend <- brick_comp |>
select(-c(.model, Bricks, trend, season_year, remainder))
brick_trend |>
model(NAIVE(season_adjust)) |>
forecast( h = "5 years") |>
autoplot(brick_trend) +
labs(title = "Seasonally adjusted Naive forecast", y = "Bricks")
tourism contains quarterly visitor nights (in thousands) from 1998 to 2017 for 76 regions of Australia.
Extract data from the Gold Coast region using filter() and aggregate total overnight trips (sum over Purpose) using summarise(). Call this new dataset gc_tourism.
gc_tourism <- tourism |>
filter(Region == "Gold Coast") |>
group_by(Purpose) |>
summarise(Total_Overnight_Trips = sum(Trips, na.rm = TRUE))
range(gc_tourism$Quarter)## <yearquarter[2]>
## [1] "1998 Q1" "2017 Q4"
## # Year starts on: Januarygc_train_1 <- gc_tourism |>
slice(1:(n()-4))
gc_train_2 <- gc_tourism |>
slice(1:(n()-8))
gc_train_3 <- gc_tourism |>
slice(1:(n()-12))
gc_train_1## # A tsibble: 316 x 3 [1Q]
## # Key: Purpose [4]
## Purpose Quarter Total_Overnight_Trips
## <chr> <qtr> <dbl>
## 1 Business 1998 Q1 65.5
## 2 Business 1998 Q2 70.8
## 3 Business 1998 Q3 110.
## 4 Business 1998 Q4 111.
## 5 Business 1999 Q1 98.0
## 6 Business 1999 Q2 61.3
## 7 Business 1999 Q3 121.
## 8 Business 1999 Q4 104.
## 9 Business 2000 Q1 95.2
## 10 Business 2000 Q2 84.9
## # ℹ 306 more rowsgc_train_2## # A tsibble: 312 x 3 [1Q]
## # Key: Purpose [4]
## Purpose Quarter Total_Overnight_Trips
## <chr> <qtr> <dbl>
## 1 Business 1998 Q1 65.5
## 2 Business 1998 Q2 70.8
## 3 Business 1998 Q3 110.
## 4 Business 1998 Q4 111.
## 5 Business 1999 Q1 98.0
## 6 Business 1999 Q2 61.3
## 7 Business 1999 Q3 121.
## 8 Business 1999 Q4 104.
## 9 Business 2000 Q1 95.2
## 10 Business 2000 Q2 84.9
## # ℹ 302 more rowsgc_train_3## # A tsibble: 308 x 3 [1Q]
## # Key: Purpose [4]
## Purpose Quarter Total_Overnight_Trips
## <chr> <qtr> <dbl>
## 1 Business 1998 Q1 65.5
## 2 Business 1998 Q2 70.8
## 3 Business 1998 Q3 110.
## 4 Business 1998 Q4 111.
## 5 Business 1999 Q1 98.0
## 6 Business 1999 Q2 61.3
## 7 Business 1999 Q3 121.
## 8 Business 1999 Q4 104.
## 9 Business 2000 Q1 95.2
## 10 Business 2000 Q2 84.9
## # ℹ 298 more rowsCompute one year of forecasts for each training set using the seasonal naïve (SNAIVE()) method. Call these gc_fc_1, gc_fc_2 and gc_fc_3, respectively.
gc_tourism <- tourism |>
filter(Region == "Gold Coast") |>
group_by(Purpose) |>
summarise(Total_Overnight_Trips = sum(Trips, na.rm = TRUE))
range(gc_tourism$Quarter)## <yearquarter[2]>
## [1] "1998 Q1" "2017 Q4"
## # Year starts on: Januarygc_train_1 <- gc_tourism |>
slice(1:(n()-4))
gc_train_2 <- gc_tourism |>
slice(1:(n()-8))
gc_train_3 <- gc_tourism |>
slice(1:(n()-12))
gc_train_1## # A tsibble: 316 x 3 [1Q]
## # Key: Purpose [4]
## Purpose Quarter Total_Overnight_Trips
## <chr> <qtr> <dbl>
## 1 Business 1998 Q1 65.5
## 2 Business 1998 Q2 70.8
## 3 Business 1998 Q3 110.
## 4 Business 1998 Q4 111.
## 5 Business 1999 Q1 98.0
## 6 Business 1999 Q2 61.3
## 7 Business 1999 Q3 121.
## 8 Business 1999 Q4 104.
## 9 Business 2000 Q1 95.2
## 10 Business 2000 Q2 84.9
## # ℹ 306 more rowsgc_train_2## # A tsibble: 312 x 3 [1Q]
## # Key: Purpose [4]
## Purpose Quarter Total_Overnight_Trips
## <chr> <qtr> <dbl>
## 1 Business 1998 Q1 65.5
## 2 Business 1998 Q2 70.8
## 3 Business 1998 Q3 110.
## 4 Business 1998 Q4 111.
## 5 Business 1999 Q1 98.0
## 6 Business 1999 Q2 61.3
## 7 Business 1999 Q3 121.
## 8 Business 1999 Q4 104.
## 9 Business 2000 Q1 95.2
## 10 Business 2000 Q2 84.9
## # ℹ 302 more rowsgc_train_3## # A tsibble: 308 x 3 [1Q]
## # Key: Purpose [4]
## Purpose Quarter Total_Overnight_Trips
## <chr> <qtr> <dbl>
## 1 Business 1998 Q1 65.5
## 2 Business 1998 Q2 70.8
## 3 Business 1998 Q3 110.
## 4 Business 1998 Q4 111.
## 5 Business 1999 Q1 98.0
## 6 Business 1999 Q2 61.3
## 7 Business 1999 Q3 121.
## 8 Business 1999 Q4 104.
## 9 Business 2000 Q1 95.2
## 10 Business 2000 Q2 84.9
## # ℹ 298 more rowsgc_fc_1 <- gc_train_1 |>
model(SNAIVE(Total_Overnight_Trips)) |>
forecast( h = 4)
gc_fc_1 |>
autoplot(gc_train_1) +
labs(title = "GC Train 1 SNaive Forecast")
gc_fc_2 <- gc_train_2 |>
model(SNAIVE(Total_Overnight_Trips)) |>
forecast( h = 4)
gc_fc_2 |> autoplot(gc_train_2) +
labs(title = "GC Train 2 SNaive Forecast")
gc_fc_3 <- gc_train_3 |>
model(SNAIVE(Total_Overnight_Trips)) |>
forecast( h = 4)
gc_fc_3 |> autoplot(gc_train_3) +
labs(title = "GC Train 3 SNaive Forecast")
gc_fc_1 |> accuracy(gc_tourism)## Warning: The future dataset is incomplete, incomplete out-of-sample data will be treated as missing.
## 4 observations are missing between 2018 Q1 and 2018 Q4## # A tibble: 4 × 11
## .model Purpose .type ME RMSE MAE MPE MAPE MASE RMSSE ACF1
## <chr> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 SNAIVE(Tota… Busine… Test NaN NaN NaN NaN NaN NaN NaN NA
## 2 SNAIVE(Tota… Holiday Test NaN NaN NaN NaN NaN NaN NaN NA
## 3 SNAIVE(Tota… Other Test NaN NaN NaN NaN NaN NaN NaN NA
## 4 SNAIVE(Tota… Visiti… Test 20.4 64.2 59.0 5.41 17.8 1.39 1.20 -0.574gc_fc_2 |> accuracy(gc_tourism)## Warning: The future dataset is incomplete, incomplete out-of-sample data will be treated as missing.
## 4 observations are missing between 2018 Q1 and 2018 Q4## # A tibble: 4 × 11
## .model Purpose .type ME RMSE MAE MPE MAPE MASE RMSSE ACF1
## <chr> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 SNAIVE(To… Busine… Test NaN NaN NaN NaN NaN NaN NaN NA
## 2 SNAIVE(To… Holiday Test NaN NaN NaN NaN NaN NaN NaN NA
## 3 SNAIVE(To… Other Test NaN NaN NaN NaN NaN NaN NaN NA
## 4 SNAIVE(To… Visiti… Test 7.05 53.9 47.2 0.253 15.7 1.12 1.01 -0.724gc_fc_3 |> accuracy(gc_tourism)## Warning: The future dataset is incomplete, incomplete out-of-sample data will be treated as missing.
## 4 observations are missing between 2018 Q1 and 2018 Q4## # A tibble: 4 × 11
## .model Purpose .type ME RMSE MAE MPE MAPE MASE RMSSE ACF1
## <chr> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 SNAIVE(T… Busine… Test NaN NaN NaN NaN NaN NaN NaN NA
## 2 SNAIVE(T… Holiday Test NaN NaN NaN NaN NaN NaN NaN NA
## 3 SNAIVE(T… Other Test NaN NaN NaN NaN NaN NaN NaN NA
## 4 SNAIVE(T… Visiti… Test 13.3 28.4 24.9 5.20 8.84 0.575 0.520 -0.251It’s clear that the gc_fc_3 has the lowest MAPE. This is due removing the last 3 years of observations.