A quantitative analyst is modeling a company's monthly sales data from the last decade. A time series plot reveals a consistent upward trend, and an Augmented Dickey-Fuller (ADF) test confirms the series is non-stationary. The analyst plans to use an Autoregressive Integrated Moving Average (ARIMA) model for forecasting. To address the identified non-stationarity, which configuration choice for the ARIMA(p, d, q) model is the most critical first step?
Set the differencing order, d, to a value of 1 or more to make the series stationary.
Determine the autoregressive order, p, by examining the Partial Autocorrelation Function (PACF) of the original series.
Apply a Box-Cox transformation to the series to remove the stochastic trend.
Select the moving average order, q, by inspecting the Autocorrelation Function (ACF) of the original series.
The correct answer is to set the differencing order, d, to a value of 1 or more. The 'I' in ARIMA stands for 'Integrated' and represents the differencing applied to the raw observations to make the time series stationary. Since the ADF test confirmed the series is non-stationary due to a trend, applying one or more orders of differencing (setting d >= 1) is the essential first step to stabilize the mean of the series. Only after the series is stationary should the analyst examine the ACF and PACF plots of the differenced series to determine the appropriate p and q values. Analyzing the ACF and PACF plots of the original, non-stationary series would be misleading. A Box-Cox transformation is used to stabilize non-constant variance (heteroskedasticity), not to remove a trend, which is a form of non-stationarity in the mean.
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What does 'd' in ARIMA(p, d, q) represent?
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What is the purpose of the Augmented Dickey-Fuller (ADF) test?
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Why can't we use the ACF and PACF plots of a non-stationary series to determine 'p' and 'q'?