DSE Time Series Analysis and Forecasting 1 — Questions and Answers
Question 1: What property of a time series indicates that its statistical properties such as mean and variance remain constant over time?
- Autocorrelation
- Stationarity (Correct answer)
- Seasonality
- Heteroscedasticity
Correct answer: Stationarity
Stationarity means a time series has constant mean, variance, and autocovariance over time, which is required by many standard forecasting models.
Question 2: Which statistical test is most commonly used to check whether a time series is stationary by testing for a unit root?
- Chi-square test
- F-test
- Augmented Dickey-Fuller (ADF) test (Correct answer)
- Shapiro-Wilk test
Correct answer: Augmented Dickey-Fuller (ADF) test
The Augmented Dickey-Fuller test checks for a unit root in a time series; failing to reject the null hypothesis indicates the series is non-stationary.
Question 3: What does the Autocorrelation Function (ACF) measure in time series analysis?
- The correlation between two different time series
- The correlation between a time series and a lagged version of itself (Correct answer)
- The rate of change in a time series over time
- The strength of seasonal patterns in a time series
Correct answer: The correlation between a time series and a lagged version of itself
The ACF measures the correlation between a time series and its own lagged values at different time lags, helping identify patterns and the order of MA terms.
Question 4: What is the primary purpose of differencing in time series analysis?
- To remove outliers from the data
- To add seasonal components to the model
- To make a non-stationary series stationary (Correct answer)
- To smooth random fluctuations
Correct answer: To make a non-stationary series stationary
Differencing subtracts each observation from the previous one, eliminating trends and transforming a non-stationary series into a stationary one.
Question 5: In classical time series decomposition, which component represents patterns that repeat at fixed, known intervals such as monthly or yearly cycles?
- Trend component
- Residual component
- Cyclic component
- Seasonal component (Correct answer)
Correct answer: Seasonal component
The seasonal component captures repeating patterns at fixed, known intervals (e.g., higher retail sales every December), distinct from longer irregular cyclic swings.
Question 6: In time series analysis, what characterizes a 'white noise' series?
- A series with a strong upward trend
- A series with high seasonality and regular cycles
- A series of uncorrelated observations with zero mean and constant variance (Correct answer)
- A series that has been differenced exactly once
Correct answer: A series of uncorrelated observations with zero mean and constant variance
White noise consists of uncorrelated random variables with zero mean and constant variance, representing ideal residuals after all systematic patterns have been modeled.
Question 7: What does the 'I' in ARIMA stand for, and what does it indicate about the model?
- Integrated — the number of differencing operations applied to achieve stationarity (Correct answer)
- Independent — that the error terms are independent of each other
- Interval — the time interval between observations
- Inversed — that the series has been log-transformed
Correct answer: Integrated — the number of differencing operations applied to achieve stationarity
In ARIMA (AutoRegressive Integrated Moving Average), 'I' stands for Integrated, referring to the order d — how many times the series is differenced to become stationary.
DSE Time Series Analysis and Forecasting 1
What property of a time series indicates that its statistical properties such as mean and variance remain constant over time?