Data Science Time Series Analysis 1 — Questions and Answers
Question 1: In time series analysis, a series is considered stationary if:
- Its mean, variance, and autocovariance are constant over time (Correct answer)
- It has no seasonal patterns whatsoever
- Its values are always positive
- Its values always increase over time
Correct answer: Its mean, variance, and autocovariance are constant over time
A stationary time series has constant statistical properties (mean, variance, and autocovariance) over time, which is required by most classical time series models.
Question 2: What does the Autocorrelation Function (ACF) measure in a time series?
- The correlation between two completely different time series
- The correlation between a time series and a lagged version of itself (Correct answer)
- The variance of the time series at each individual time point
- The trend direction of the time series over the full period
Correct answer: The correlation between a time series and a lagged version of itself
The ACF measures the linear correlation between a time series and its own past values at various lags, helping identify repeating patterns and appropriate model parameters.
Question 3: What does the 'I' stand for in the ARIMA model?
- Independent
- Interaction
- Integrated (Correct answer)
- Interval
Correct answer: Integrated
The 'I' in ARIMA stands for 'Integrated,' referring to the differencing of the series to achieve stationarity before fitting the AR and MA components.
Question 4: What is seasonality in a time series?
- Long-term upward or downward movement in the data
- Random fluctuations with no predictable pattern
- Regular, periodic patterns that repeat at fixed time intervals (Correct answer)
- A sudden structural change in the mean level of the series
Correct answer: Regular, periodic patterns that repeat at fixed time intervals
Seasonality refers to regular, repeating fluctuations that occur at fixed intervals such as daily, weekly, or yearly cycles — driven by factors like weather or business calendars.
Question 5: The Partial Autocorrelation Function (PACF) is primarily used to determine:
- The order of the Moving Average (MA) component
- The order of the Autoregressive (AR) component (Correct answer)
- Whether the series is stationary or needs differencing
- The optimal forecasting horizon for the model
Correct answer: The order of the Autoregressive (AR) component
PACF measures the direct correlation between a series and its lags after removing the effect of intermediate lags, which helps identify the appropriate AR order (p) in ARIMA.
Question 6: What is white noise in time series analysis?
- A sequence with a consistent upward trend over time
- Data with strong and predictable seasonal patterns
- A series of uncorrelated random variables with constant mean and variance (Correct answer)
- A series that requires differencing to become stationary
Correct answer: A series of uncorrelated random variables with constant mean and variance
White noise is a sequence of uncorrelated random variables with zero mean and constant variance — it contains no predictable structure and represents the ideal model residuals.
Question 7: What does 'trend' represent in a time series?
- Periodic fluctuations that repeat on a yearly basis
- The long-term increase or decrease in the data over an extended period (Correct answer)
- Random variation around the series mean value
- The moving average calculated across the entire series
Correct answer: The long-term increase or decrease in the data over an extended period
Trend represents the long-term, systematic directional movement (upward or downward) in the data, distinct from seasonal cycles or random noise.
Data Science Time Series Analysis 1
In time series analysis, a series is considered stationary if: