Time Series Analysis and Forecasting Flashcards
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Read the first 7 Time Series Analysis and Forecasting flashcards as text
In an ARIMA(p, d, q) model, what does the parameter 'p' represent?
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.
Which plot is used to determine the order of the autoregressive term (p) when building an ARIMA model?
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.
What is the key difference between an AR (AutoRegressive) model and an MA (Moving Average) model?
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.
What is the core principle behind exponential smoothing in time series forecasting?
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.
The Ljung-Box test applied to time series model residuals is used to test for what?
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.
How is the Akaike Information Criterion (AIC) used in ARIMA model selection?
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.
The Box-Jenkins methodology is a systematic approach primarily used for what purpose?
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.