DSE Time Series Analysis and Forecasting 2 — Questions and Answers
Question 1: In an ARIMA(p, d, q) model, what does the parameter 'p' represent?
- The degree of differencing applied to the series
- The order of the moving average component
- The order of the autoregressive component (Correct answer)
- The seasonal period of the data
Correct answer: The order of the autoregressive component
In ARIMA(p, d, q), p is the order of the AutoRegressive component, specifying how many lagged values of the series are included as predictors.
Question 2: Which plot is used to determine the order of the autoregressive term (p) when building an ARIMA model?
- ACF (Autocorrelation Function) plot
- Histogram of residuals
- PACF (Partial Autocorrelation Function) plot (Correct answer)
- Q-Q (quantile-quantile) plot
Correct answer: PACF (Partial Autocorrelation Function) plot
The PACF shows the direct correlation between a series and its lags after removing the effect of shorter intermediate lags, making it the standard tool for selecting the AR order p.
Question 3: What is the key difference between an AR (AutoRegressive) model and an MA (Moving Average) model?
- AR models use lagged forecast errors as predictors; MA models use lagged observed values
- AR models use lagged observed values as predictors; MA models use lagged forecast errors as predictors (Correct answer)
- AR models require stationarity; MA models can handle non-stationary data directly
- AR models are for seasonal data only; MA models handle non-seasonal data
Correct answer: AR models use lagged observed values as predictors; MA models use lagged forecast errors as predictors
An AR model regresses the current value on past observed values of the series, while an MA model uses past forecast errors (residuals) as its predictor inputs.
Question 4: What is the core principle behind exponential smoothing in time series forecasting?
- Detecting unit roots by testing residual autocorrelation
- Identifying the dominant seasonal period in the data
- Assigning exponentially decreasing weights to past observations so recent data has more influence (Correct answer)
- Removing autocorrelation from model residuals before forecasting
Correct answer: Assigning exponentially decreasing weights to past observations so recent data has more influence
Exponential smoothing applies geometrically declining weights to historical observations, ensuring the most recent values contribute most to the forecast.
Question 5: The Ljung-Box test applied to time series model residuals is used to test for what?
- Normality of the residual distribution
- Remaining autocorrelation in the residuals (Correct answer)
- Heteroscedasticity in the original series
- Cointegration between two time series
Correct answer: Remaining autocorrelation in the residuals
The Ljung-Box test checks whether the residuals from a fitted model show significant autocorrelation at multiple lags; significant autocorrelation means the model is inadequate.
Question 6: How is the Akaike Information Criterion (AIC) used in ARIMA model selection?
- It tests whether the series is stationary before differencing
- It measures out-of-sample forecast accuracy on a held-out test set
- It balances goodness of fit against model complexity to help avoid overfitting (Correct answer)
- It detects and flags outliers in the training data
Correct answer: It balances goodness of fit against model complexity to help avoid overfitting
AIC penalizes adding more parameters while rewarding model fit, guiding selection toward the most parsimonious ARIMA model that adequately captures the data.
Question 7: The Box-Jenkins methodology is a systematic approach primarily used for what purpose?
- Clustering time series by pattern similarity
- Identifying, estimating, and diagnostically checking ARIMA models (Correct answer)
- Decomposing a series into trend, seasonal, and residual components
- Applying deep learning to multivariate time series forecasting
Correct answer: Identifying, estimating, and diagnostically checking ARIMA models
The Box-Jenkins methodology is a three-stage process — identification, parameter estimation, and diagnostic checking — specifically designed for building ARIMA models.
DSE Time Series Analysis and Forecasting 2
In an ARIMA(p, d, q) model, what does the parameter 'p' represent?