Data Science Time Series Analysis 2 — Questions and Answers
Question 1: In ARIMA(p, d, q), what does the parameter 'd' represent?
- The degree of autocorrelation in the series
- The number of MA (moving average) terms
- The number of times the data is differenced to achieve stationarity (Correct answer)
- The number of AR (autoregressive) terms
Correct answer: The number of times the data is differenced to achieve stationarity
The 'd' parameter in ARIMA is the integration order — it specifies how many times the series must be differenced to remove non-stationarity such as trends.
Question 2: The Augmented Dickey-Fuller (ADF) test is primarily used to:
- Detect the presence of seasonality in a time series
- Test whether a time series has a unit root and is non-stationary (Correct answer)
- Select the optimal number of ARIMA parameters automatically
- Measure the out-of-sample forecasting accuracy of a model
Correct answer: Test whether a time series has a unit root and is non-stationary
The ADF test checks for a unit root in the series — rejecting the null hypothesis (unit root present) provides evidence that the series is stationary.
Question 3: In simple exponential smoothing, the smoothing parameter α controls:
- The total number of observations included in each forecast
- The weight applied to the seasonal component only
- The rate at which the influence of older observations decays (Correct answer)
- The strength of the trend component in the forecast
Correct answer: The rate at which the influence of older observations decays
α (between 0 and 1) determines how quickly past observations lose influence — a higher α means more weight on recent data and faster adaptation to changes.
Question 4: What is the primary purpose of time series decomposition?
- To remove all randomness and noise from the data entirely
- To separate the series into trend, seasonality, and residual components (Correct answer)
- To convert a non-stationary series into a stationary one for modeling
- To automatically select optimal ARIMA model parameters
Correct answer: To separate the series into trend, seasonality, and residual components
Time series decomposition breaks a series into its underlying components — trend, seasonal pattern, and irregular residuals — to better understand and model each element separately.
Question 5: A simple moving average of order k is computed as:
- The exponentially weighted sum of all past observations
- The arithmetic mean of the k most recent observations (Correct answer)
- The median of the last k observations in the series
- The weighted sum of lagged values defined by an AR model
Correct answer: The arithmetic mean of the k most recent observations
A simple moving average of order k computes the unweighted arithmetic mean of the k most recent data points, smoothing short-term fluctuations to reveal underlying trends.
Question 6: The Holt-Winters (Triple Exponential Smoothing) method is designed to handle:
- Only trend but not seasonality in a time series
- Only seasonality but not trend in the data
- Both trend and seasonality simultaneously in a time series (Correct answer)
- Strictly stationary time series with no trend or seasonality
Correct answer: Both trend and seasonality simultaneously in a time series
Holt-Winters extends simple exponential smoothing with three smoothing equations — level, trend, and seasonality — enabling it to forecast series exhibiting both patterns.
Question 7: Which forecasting accuracy metric is most appropriate when you want a scale-independent measure suitable for comparing across datasets with different magnitudes?
- Mean Absolute Error (MAE)
- Root Mean Square Error (RMSE)
- Mean Absolute Percentage Error (MAPE) (Correct answer)
- Sum of Squared Errors (SSE)
Correct answer: Mean Absolute Percentage Error (MAPE)
MAPE expresses forecast errors as a percentage of actual values, making it dimensionless and directly comparable across datasets of different scales.
Data Science Time Series Analysis 2
In ARIMA(p, d, q), what does the parameter 'd' represent?