1Which of the following best describes a Time Series dataset?
A.A dataset where the target variable is categorical and independent of time.
B.A dataset containing only images captured at different locations.
C.A sequence of data points indexed in time order, often with equal intervals.
D.A collection of data points collected from random individuals at a single point in time.
Correct Answer: A sequence of data points indexed in time order, often with equal intervals.
Explanation:
A time series is a sequence of numerical data points in successive order, usually occurring at uniform intervals (e.g., daily stock prices, hourly temperature).
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2In the context of Time Series analysis, what does Stationarity imply?
A.The statistical properties (mean, variance, covariance) are constant over time.
B.The data contains no missing values.
C.The time series has a constant trend increasing over time.
D.The seasonal component of the data is strictly periodic.
Correct Answer: The statistical properties (mean, variance, covariance) are constant over time.
Explanation:
A stationary time series is one whose statistical properties such as mean, variance, and autocorrelation are all constant over time. This is a key assumption for many models like ARIMA.
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3Which component of a time series represents a long-term increase or decrease in the data?
A.Seasonality
B.Noise (Irregularity)
C.Trend
D.Cyclicality
Correct Answer: Trend
Explanation:
The Trend represents the underlying long-term direction in the data (increasing or decreasing) over a long period, ignoring short-term fluctuations.
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4What is the difference between Univariate and Multivariate time series?
A.Univariate is for stationary data; Multivariate is for non-stationary data.
C.Univariate involves a single variable varying over time; Multivariate involves multiple variables varying over time.
D.Univariate has irregular intervals; Multivariate has regular intervals.
Correct Answer: Univariate involves a single variable varying over time; Multivariate involves multiple variables varying over time.
Explanation:
Univariate time series consists of a single sequence of observations (e.g., just temperature). Multivariate consists of multiple changing variables that may influence each other (e.g., temperature, humidity, and wind speed).
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5When preparing time series data for supervised learning, what is a Lag Feature?
A.Observation from a previous time step used as an input feature (e.g., ).
B.The difference between the current value and the mean.
C.A future value used to predict the past.
D.The error term from a moving average model.
Correct Answer: Observation from a previous time step used as an input feature (e.g., ).
Explanation:
Lag features involve shifting the time series data so that past values (e.g., ) become input features to predict the current value .
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6Which of the following is a common method to handle Irregular Intervals in time series data before modeling?
A.Ignoring the time index and treating it as cross-sectional data.
B.Using a random number generator to fill gaps.
C.Resampling or Interpolation to a fixed frequency.
D.Dropping all timestamps.
Correct Answer: Resampling or Interpolation to a fixed frequency.
Explanation:
To apply standard time series algorithms, data is often resampled (e.g., aggregation) or interpolated (e.g., linear fill) to ensure a constant time interval between observations.
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7Why is K-Fold Cross-Validation with random shuffling inappropriate for time series data?
A.Time series data is always too small for K-Fold.
B.It assumes the data is non-stationary.
C.It is too computationally expensive.
D.It causes data leakage by using future data to predict past data.
Correct Answer: It causes data leakage by using future data to predict past data.
Explanation:
Random shuffling destroys the temporal order. If you train on future data and test on past data (look-ahead bias), the model performance estimates will be overly optimistic and unrealistic.
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8What is the Walk-Forward Validation (or Time Series Split) strategy?
A.Using a sliding or expanding window where the training set consists of past data and the test set consists of immediate future data.
B.Randomly selecting 20% of the data for testing.
C.Splitting data based on the magnitude of the values.
D.Training on all data and testing on the same data.
Correct Answer: Using a sliding or expanding window where the training set consists of past data and the test set consists of immediate future data.
Explanation:
Walk-Forward Validation respects temporal order. The model is trained on a sequence of past data and evaluated on the subsequent time steps, simulating real-world forecasting.
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9Which mathematical operation is commonly used to transform a non-stationary series with a trend into a stationary one?
A.Squaring
B.Integration
C.Differencing (e.g., )
D.Multiplication
Correct Answer: Differencing (e.g., )
Explanation:
Differencing involves computing the change between consecutive observations. It stabilizes the mean of a time series by removing changes in the level of a time series, thus eliminating trend.
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10In an Autoregressive (AR) model of order , denoted as AR(), the current value is predicted based on:
A.Past forecast errors.
B.A linear combination of past values.
C.Independent external variables only.
D.A moving average of the entire dataset.
Correct Answer: A linear combination of past values.
Explanation:
An AR() model predicts the variable of interest using a linear combination of its past values: .
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11The equation represents which model?
A.AR(1)
B.ARIMA(1,1,1)
C.MA(1)
D.Random Walk
Correct Answer: MA(1)
Explanation:
This is a Moving Average model of order 1, MA(1). It models the value as a linear combination of the mean and the current and past error terms (shocks).
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12What does the 'I' in ARIMA stand for?
A.Interpolated
B.Independent
C.Integrated
D.Irregular
Correct Answer: Integrated
Explanation:
The 'I' stands for Integrated. It refers to the differencing of raw observations (subtracting an observation from an observation at the previous time step) to make the time series stationary.
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13In the notation ARIMA(p, d, q), what does the parameter represent?
A.The seasonality period.
B.The size of the moving average window.
C.The number of times that the raw observations are differenced.
D.The number of lag observations included in the model.
Correct Answer: The number of times that the raw observations are differenced.
Explanation:
is the degree of differencing required to make the time series stationary (i.e., how many times we subtract the previous value from the current value).
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14Which plot is most useful for determining the order of a Moving Average (MA) model?
A.Histogram
B.Scatter plot
C.Partial Autocorrelation Function (PACF)
D.Autocorrelation Function (ACF)
Correct Answer: Autocorrelation Function (ACF)
Explanation:
For an MA() process, the ACF cuts off after lag . Thus, the ACF plot is used to identify the order of the MA component.
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15Which plot is most useful for determining the order of an Autoregressive (AR) model?
A.Autocorrelation Function (ACF)
B.Partial Autocorrelation Function (PACF)
C.Spectral Density Plot
D.Box Plot
Correct Answer: Partial Autocorrelation Function (PACF)
Explanation:
For an AR() process, the PACF cuts off after lag , while the ACF tails off. Therefore, PACF is used to determine the AR order.
SARIMA (Seasonal ARIMA) extends ARIMA by adding seasonal autoregressive and moving average terms to handle data with repeating cycles (seasonality).
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17In SARIMA notation , what does represent?
A.The maximum value of the series.
B.The number of time steps for a single seasonal period.
C.The number of features.
D.The order of the polynomial trend.
Correct Answer: The number of time steps for a single seasonal period.
Explanation:
refers to the periodicity of the seasonality (e.g., for monthly data with a yearly cycle, for daily data with a weekly cycle).
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18If a time series is a White Noise process, which of the following is true?
A.It can be perfectly predicted using linear regression.
B.It strictly follows a sinusoidal wave.
C.It has zero autocorrelation for all lags .
D.Its mean and variance change rapidly over time.
Correct Answer: It has zero autocorrelation for all lags .
Explanation:
White noise is a sequence of random numbers with constant mean (usually 0), constant variance, and no correlation between values at different times (uncorrelated).
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19What is the primary risk of using standard Min-Max Scaling on the entire dataset before splitting into train/test in time series?
A.It introduces Lookahead Bias (Data Leakage).
B.It makes the data non-stationary.
C.It changes the time order.
D.It removes the seasonality.
Correct Answer: It introduces Lookahead Bias (Data Leakage).
Explanation:
If you scale using the min/max of the whole dataset, the training data contains information about the range of the future test data. Scaling should be fitted only on the training set.
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20Which test is commonly used to check for Stationarity?
A.ANOVA
B.Chi-Square test
C.Augmented Dickey-Fuller (ADF) test
D.T-test
Correct Answer: Augmented Dickey-Fuller (ADF) test
Explanation:
The ADF test checks the null hypothesis that a unit root is present in a time series sample (indicating non-stationarity). A low p-value indicates the series is stationary.
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21Consider the equation: . This is an example of:
A.MA(1) process.
B.Stationary AR(1) process.
C.Explosive AR(1) process.
D.AR(1) with unit root.
Correct Answer: Stationary AR(1) process.
Explanation:
This is an AR(1) process . Since the absolute value of the coefficient , the process is stationary.
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22In the context of Time Series Regression, what are Exogenous Variables?
A.Variables representing the error term.
B.Internal lag variables derived from the target.
C.Variables that are predicted by the model.
D.External variables that influence the target but are not influenced by it.
Correct Answer: External variables that influence the target but are not influenced by it.
Explanation:
Exogenous variables (often denoted as in ARIMAX) are parallel input time series that help explain the behavior of the target variable (e.g., Temperature helping to predict Ice Cream Sales).
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23If a time series exhibits a variance that increases over time (heteroscedasticity), which transformation is commonly applied to stabilize variance?
A.Standardization
B.Logarithmic Transformation
C.Adding a constant
D.Differencing
Correct Answer: Logarithmic Transformation
Explanation:
Taking the log of a time series is a standard technique to linearize exponential trends and stabilize variance (homoscedasticity) when fluctuations grow with the level of the series.
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24What is an Expanding Window split strategy?
A.The test set size grows while the training set shrinks.
B.The training set size remains constant and slides forward.
C.Data is shuffled and split randomly.
D.The training set starts small and grows in size as new data becomes available.
Correct Answer: The training set starts small and grows in size as new data becomes available.
Explanation:
In an expanding window, the training set effectively accumulates all prior data up to the current split point, retaining the entire history, unlike a sliding window which drops old data.
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25What is the consequence of Over-differencing a time series?
A.It increases the variance of the trend.
B.The series becomes perfectly linear.
C.It makes the trend more pronounced.
D.It introduces artificial noise and negative autocorrelation.
Correct Answer: It introduces artificial noise and negative autocorrelation.
Explanation:
Differencing a series that is already stationary creates a new series with increased variance and artificial dependencies (specifically negative autocorrelation at lag 1), complicating modeling.
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26Which of the following describes a Random Walk model?
A.ARIMA(1, 0, 0)
B.ARIMA(0, 0, 1)
C.ARIMA(1, 1, 1)
D.ARIMA(0, 1, 0)
Correct Answer: ARIMA(0, 1, 0)
Explanation:
A Random Walk is defined as , or . This corresponds to an ARIMA model with differencing order and no AR or MA terms ().
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27In an AR(1) model , if , the series is:
A.White Noise
B.Stationary
C.A Random Walk (Non-stationary)
D.Mean reverting
Correct Answer: A Random Walk (Non-stationary)
Explanation:
If the coefficient is 1, a unit root exists. The value depends entirely on the previous value plus a shock, and variances accumulate over time, making it non-stationary.
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28Which metric provides a penalty for adding parameters to a model, helping to avoid overfitting in ARIMA model selection?
A.R-Squared
B.MSE (Mean Squared Error)
C.MAE (Mean Absolute Error)
D.AIC (Akaike Information Criterion)
Correct Answer: AIC (Akaike Information Criterion)
Explanation:
AIC estimates the quality of a model relative to others. It includes a term representing the likelihood and a penalty term for the number of parameters (), discouraging unnecessary complexity.
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29For a monthly time series with strong yearly seasonality, what is the value of the seasonal period parameter ?
A.30
B.12
C.4
D.7
Correct Answer: 12
Explanation:
Monthly data repeats a cycle every year, so the period (or ) is 12.
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30What is Seasonal Differencing?
A.
B.
C.
D. where is the seasonal period.
Correct Answer: where is the seasonal period.
Explanation:
Seasonal differencing subtracts the value from the same season in the previous cycle (e.g., this January minus last January) to remove seasonal components.
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31A model defined as is an:
A.ARMA(1,1)
B.AR(1)
C.AR(2)
D.MA(2)
Correct Answer: AR(2)
Explanation:
This model relies on two previous time steps ( and ), making it an Autoregressive model of order 2.
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32The Ljung-Box Test is applied to the residuals of a time series model to check:
A.If the residuals differ significantly from white noise (i.e., if there is remaining autocorrelation).
B.If the model parameters are statistically significant.
C.If the original data was stationary.
D.If the residuals are normally distributed.
Correct Answer: If the residuals differ significantly from white noise (i.e., if there is remaining autocorrelation).
Explanation:
The Ljung-Box test checks if the autocorrelations of the residuals are non-zero. If p-value < 0.05, residuals are not white noise, implying the model failed to capture some structure.
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33How are missing values typically handled in time series if dropping them is not an option?
A.Time-based interpolation (e.g., linear) or Forward Fill.
B.Replace with the dataset maximum.
C.Replace with the dataset standard deviation.
D.Replace with zero.
Correct Answer: Time-based interpolation (e.g., linear) or Forward Fill.
Explanation:
Since time series data is continuous, methods like Forward Fill (carrying the last valid observation forward) or Linear Interpolation utilize the temporal relationship to estimate missing values.
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34Which component is represented by in SARIMA?
A.Seasonal Autoregressive order
B.Seasonal Moving Average order
C.Trend Differencing order
D.Seasonal Differencing order
Correct Answer: Seasonal Differencing order
Explanation:
Capital represents the order of seasonal differencing applied to the series.
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35If the ACF plot decays slowly (linear decay) while the PACF shows a sharp cutoff at lag 1, the series is likely:
A.AR(1)
B.MA(1)
C.White Noise
D.ARMA(1,1)
Correct Answer: AR(1)
Explanation:
This is the signature behavior of an AR process. An AR() process has a PACF that cuts off at lag and an ACF that tails off.
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36In time series regression, what is a Rolling Window feature?
A.A window that randomly selects features.
B.A feature computed by aggregating (mean, max, etc.) values over a fixed-size window of past observations.
C.A technique to increase the sampling rate.
D.A feature that looks into the future.
Correct Answer: A feature computed by aggregating (mean, max, etc.) values over a fixed-size window of past observations.
Explanation:
Rolling window statistics (e.g., 7-day moving average) summarize recent history to capture local trends or volatility as input features.
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37Which of the following equations represents an ARIMA(1,1,1) model (excluding constant)? Let .
A.
B.
C.
D.
Correct Answer:
Explanation:
ARIMA(1,1,1) implies differencing (). The model is then an ARMA(1,1) on the differenced series .
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38When encoding cyclical time features like 'Month of Year' (1-12) for regression, what is the best approach to preserve the cycle (i.e., Dec is close to Jan)?
A.Sine and Cosine transformation
B.One-Hot Encoding
C.Label Encoding (1, 2, ..., 12)
D.Binary Encoding
Correct Answer: Sine and Cosine transformation
Explanation:
Using Sin/Cos transformations maps the cyclic feature onto a circle, ensuring that the distance between Month 12 and Month 1 is small, preserving the cyclical nature.
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39What is Naive Forecasting?
A.Using a complex neural network.
B.Predicting the value at time to be equal to the value at time .
C.Predicting zero for all future steps.
D.Predicting the current value as the average of all past values.
Correct Answer: Predicting the value at time to be equal to the value at time .
Explanation:
Naive forecasting assumes that the next observation will be exactly the same as the most recent observation (). It is often used as a baseline.
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40What is the key assumption of the Moving Average (MA) model regarding shocks/errors?
A.Current value depends on past values of the variable.
B.Current value depends on current and past unobserved white noise error terms.
C.Errors increase exponentially with time.
D.Errors are correlated with the independent variables.
Correct Answer: Current value depends on current and past unobserved white noise error terms.
Explanation:
MA models conceptualize the series as being driven by a sequence of random shocks (errors). The current value is a weighted sum of recent shocks.
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41In the context of SARIMA, what is an Exogenous regressor often denoted as?
A.ARIMAE
B.ARIMAS
C.XY-ARIMA
D.SARIMAX
Correct Answer: SARIMAX
Explanation:
The 'X' in SARIMAX or ARIMAX stands for eXogenous variables, allowing the inclusion of external predictors.
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42If a time series has a unit root, the series is:
A.Stationary
B.Non-Stationary
C.Deterministic
D.Seasonal
Correct Answer: Non-Stationary
Explanation:
A unit root indicates that the characteristic equation of the AR process has a root of 1, meaning shocks have a permanent effect, resulting in non-stationarity.
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43Which ARIMA model is theoretically equivalent to Simple Exponential Smoothing?
A.ARIMA(0,0,0)
B.ARIMA(0,1,1)
C.ARIMA(1,0,0)
D.ARIMA(2,2,2)
Correct Answer: ARIMA(0,1,1)
Explanation:
Simple Exponential Smoothing is mathematically equivalent to an ARIMA(0,1,1) model (a random walk with MA(1) error).
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44What is the purpose of Auto-Regressive terms in a model?
A.To model the relationship between an observation and a lagged observation.
B.To remove seasonality.
C.To model the relationship between an observation and a residual error.
D.To integrate the time series.
Correct Answer: To model the relationship between an observation and a lagged observation.
Explanation:
Auto-Regressive (AR) terms capture the momentum or mean-reversion by modeling the current value as a function of its own past values.
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45Why is it important to examine the Residuals of a fitted time series model?
A.To ensure they resemble random white noise.
B.To ensure they have high autocorrelation.
C.To ensure they are all positive.
D.To ensure they follow a clear trend.
Correct Answer: To ensure they resemble random white noise.
Explanation:
If residuals are white noise (uncorrelated, mean 0), it indicates the model has successfully captured all the signal (pattern) in the data. Any pattern left in residuals means the model can be improved.
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46What implies that a Time Series is Deterministic?
A.It contains a stochastic component.
B.It can be perfectly predicted by a mathematical function of time (e.g., ).
C.It is a random walk.
D.It has infinite variance.
Correct Answer: It can be perfectly predicted by a mathematical function of time (e.g., ).
Explanation:
A deterministic trend is consistent and predictable (like a perfect line or sine wave), containing no random/stochastic variation.
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47In a Multi-step forecast strategy, what is the 'Direct' method?
A.Using only the most recent observation.
B.Building a separate model for each future time step to be predicted.
C.Ideally predicting one step ahead and using that prediction for the next step.
D.Averaging the results of AR and MA models.
Correct Answer: Building a separate model for each future time step to be predicted.
Explanation:
The Direct strategy builds specific models for specific horizons (e.g., one model predicts , another predicts ), avoiding error accumulation found in recursive methods.
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48What is the 'Recursive' (or Iterative) multi-step forecast strategy?
A.Predicting , then using that prediction as input to predict , and so on.
B.Training on future data.
C.Using a different algorithm for every step.
D.Predicting all steps simultaneously using a vector output.
Correct Answer: Predicting , then using that prediction as input to predict , and so on.
Explanation:
The recursive strategy uses a single model. It predicts the next step, appends the prediction to the history, and uses the updated history to predict the subsequent step.
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49Which transformation is the inverse of Differencing?
A.Logarithm
B.Cumulative Sum (Integration)
C.Exponentiation
D.Differentiation
Correct Answer: Cumulative Sum (Integration)
Explanation:
If data was differenced to achieve stationarity for modeling, the predictions must be integrated (cumulative sum) to return them to the original scale.
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50When is an ARIMA model considered Invertible?
A.When .
B.When it can be rewritten as an infinite AR process.
C.When the AR polynomial roots lie inside the unit circle.
D.When the MA polynomial roots lie outside the unit circle.
Correct Answer: When it can be rewritten as an infinite AR process.
Explanation:
Invertibility is a property of MA processes. An MA process is invertible if it can be written as an AR() process, which requires the roots of the MA characteristic equation to lie outside the unit circle (or absolute coefficients sum < 1 in simple cases).