The Covid19 pandemic had, and unfortunately still have, a significant impact on most of the major industries. While for some sectors, the impact was positive (such as online retails, internet and steaming providers, etc.), it was negative for others (such as transportation, tourism, entertainment, etc.). In both cases, we can leverage time series modeling to quantify the effect of the Covid19 on the sector.
One simplistic approach for quantifying the impact of the pandemic (whether it is positive or negative) would include the following steps:
Analyzing the data
Before we forecast the series, let’s run a quick exploratory analysis on the series to identify its main characteristics. We will use the TSstudio package to visualize the pre_covid
series. Note that the package does not support, yet, the tsibble
object. Therefore, we will convert the series into a ts
object first:
ts.obj <- ts(pre_covid$y, start = c(2005, 7), frequency = 12)
The series before the outbreak of the pandemic:
ts_plot(ts.obj,
title = "Total Number of Air Passengers - SFO Airport",
Ytitle = "Number of Passengers",
slider = TRUE)
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Like most series that describes monthly air passenger traffic, the series has a strong monthly seasonal pattern and a positive trend. You can also notice that the seasonal component’s oscillation has become larger since 2017 (compared to previous years). Let’s use the ts_seasonal
function to create a seasonal plot of the series:
ts_seasonal(ts.obj = ts.obj, type = "all")
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As can see in the seasonal plot, the monthly seasonal effect kept overtime while the series continue to grow from year to year.
Similarly, we can review the series correlation with its past lags using the ACF and PACF functions:
ts_cor(ts.obj = ts.obj, lag.max = 36)
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And as expected, we can see strong correlation between the series and the first and seasonal lags. We will leverage this information to select time-series models for seasonal data.
Forecast the Pre-Covid19 series
One of my favorite forecasting strategies is a combination of horse racing between different time series models and backtesting as a training approach. Backtesting is the time series equivalent of the machine learning cross-validation training approach. The idea here is simple - test each model with backtesting, and select the one that performed best, on average, on the different testing partition.
The train_model
function from the TSstudio package enables us to apply this strategy seamlessly using models from the forecast and stats packages. For simplicity, we will use different flavors of ETS
and Holt-Winters
models and out-of-the-box auto.arima
and tslm
models. For the backtesting, we will split the series into 6 testing partitions, each 12 months spaced by 3 months from each other.
The methods
argument defines the models to use and the train_method
argument defines the setting of the backtesting. Can find more details about the function here.
methods <- list(ets1 = list(method = "ets",
method_arg = list(opt.crit = "lik"),
notes = "ETS model opt.crit=lik"),
ets2 = list(method = "ets",
method_arg = list(opt.crit = "amse"),
notes = "ETS model opt.crit=amse"),
ets3 = list(method = "ets",
method_arg = list(opt.crit = "mse"),
notes = "ETS model opt.crit=mse"),
auto_arima = list(method = "auto.arima",
notes = "Auto ARIMA"),
hw1 = list(method = "HoltWinters",
method_arg = NULL,
notes = "HoltWinters Model"),
hw2 = list(method = "HoltWinters",
method_arg = list(seasonal = "multiplicative"),
notes = "HW with multip. seasonality"),
tslm = list(method = "tslm",
method_arg = list(formula = input ~ trend + season),
notes = "tslm with trend and seasonal"))
train_method = list(partitions = 6,
sample.out = 12,
space = 3)
After we defined the methods and train_method
arguments we will use the train_model
function to train the models. Note that the forecast horizon is set the the length of the post_covid
series. In addition we will set the MAPA
as the error metric to evaluate the performance of the different models on the testing partitions:
md <- train_model(input = ts.obj,
methods = methods,
train_method = train_method,
horizon = nrow(post_covid),
error = "MAPE")
## # A tibble: 7 x 7
## model_id model notes avg_mape avg_rmse `avg_coverage_80%` `avg_coverage_95%`
##
## 1 hw1 HoltWinters HoltWinters Model 0.0277 149046. 0.792 0.958
## 2 ets2 ets ETS model opt.crit=amse 0.0284 161754. 0.792 0.972
## 3 hw2 HoltWinters HW with multip. seasonality 0.0300 171702. 0.528 0.847
## 4 ets1 ets ETS model opt.crit=lik 0.0307 173337. 0.833 0.958
## 5 ets3 ets ETS model opt.crit=mse 0.0311 174238. 0.861 0.972
## 6 auto_arima auto.arima Auto ARIMA 0.0334 184381. 0.597 0.889
## 7 tslm tslm tslm with trend and seasonal 0.0370 223194. 0.569 0.75
Based on the leaderboard
table from the train_model
function, the model that performed best on average on the different testing partitions is the Holt-Winters model (first version - hw1
). The model achieved, on average, the lowest MAPE (2.76%) and RMSE (149046) compared to the other models which evaluated. In addition, the model achieved a close to perfect coverage of the model prediction intervals with an average coverage of 79.2% and 95.8% for the 80% and 95% prediction interval, respectively. We can review the error distribution across the different partitions for each model with the plot_error
function:
plot_error(md)
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The plot_model
enables us to animate the forecasted values of each model on the different testing partitions of the backtesting:
plot_model(md)
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We will select the Holt-Winters model (hw1
) to calculate the Covid19 effect. We will add the selected forecast to the post_covid
dataset:
post_covid$yhat <- as.numeric(md$forecast$hw1$forecast$mean)
post_covid$upper95 <- as.numeric(md$forecast$hw1$forecast$upper[,2])
post_covid$lower95 <- as.numeric(md$forecast$hw1$forecast$lower[,2])
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