SECTION A – Very Short Answer Type
(2 × 10 = 20 Marks)
a) Different types of data used in time series analysis
The main types are time series data (observations over time), cross-sectional data (data at one point in time), and panel data (combination of time series and cross-sectional data).
b) Autocorrelation
Autocorrelation measures the correlation between current and past values of a time series. It helps identify dependence across time lags.
c) Metrics to evaluate forecasting performance
Common metrics include MAE (Mean Absolute Error), MSE (Mean Squared Error), RMSE, and MAPE, which measure forecast accuracy.
d) Purpose of plotting smoothed data
Smoothed data helps remove random noise and clearly reveal trend and seasonal patterns in a time series.
e) Least squares estimation
Least squares estimation finds model parameters by minimizing the sum of squared errors between observed and predicted values.
f) Variable selection methods in regression
Methods include forward selection, backward elimination, and stepwise regression, used to choose the most relevant variables.
g) Identifying order of ARIMA model
The order is identified using ACF and PACF plots along with differencing tests for stationarity.
h) Stationarity in ARMA models
A time series is stationary if its mean, variance, and autocovariance remain constant over time.
i) Seasonal ARIMA model
Seasonal ARIMA (SARIMA) extends ARIMA by including seasonal autoregressive and moving average terms.
j) Vector AR models
Vector Autoregressive (VAR) models capture interdependencies among multiple time series by modeling each variable using past values of all variables.
SECTION B – Long Answer Type
(Attempt any three – 10 Marks each)
2(a) Time Series and Its Components
A time series is a sequence of observations recorded at regular time intervals.
Components:
Trend – Long-term movement (e.g., increasing sales)
Seasonality – Regular periodic fluctuations (e.g., festival sales)
Cyclic changes – Long-term economic cycles
Irregular component – Random, unpredictable variations
These components help analysts understand patterns and improve forecasting accuracy.
2(b) Standard Approach to Time Series Forecasting
Steps include: Graphical analysis
Data cleaning and transformation Stationarity checking
Model identification (AR, MA, ARIMA) Parameter estimation
Diagnostic checking Forecast generation
This structured approach ensures reliable forecasts.
2(c) Model Adequacy Checking in Linear Regression
Adequacy checking ensures that assumptions are satisfied:
Residual analysis Normality tests
Homoscedasticity tests Autocorrelation checks
If violations exist, transformations or alternative models are applied.
2(d) Strengths and Limitations of ARIMA Forecasts
Strengths: Effective for short-term forecasting
Flexible and data-driven
Limitations: Requires stationary data
Weak for long-term forecasts Does not handle external variables directly
2(e) Predicting with Seasonal ARIMA
SARIMA incorporates seasonal patterns using past seasonal data.
Examples: Monthly electricity consumption
Quarterly sales Daily temperature patterns
It improves forecasts where seasonality is strong.
SECTION C – Descriptive Answer Type
3(a) Nature and Uses of Forecasting
Forecasting predicts future values based on historical data.
Uses: Business planning
Demand forecasting Weather prediction
Stock market analysis Inventory control
Forecasting supports better decision-making and risk management.
3(b) Forecasting Process
Steps include: Data collection
Data preprocessing Model selection
Model estimation Validation
Forecast output
Resources required include historical data, computational tools, and domain expertise.
4(a) General Framework for Time Series Forecasting
The framework includes: Exploratory data analysis
Stationarity testing Model identification
Parameter estimation Diagnostic checking
Forecast generation
This ensures a systematic forecasting approach.
4(b) Need for Data Transformations
Transformations such as differencing, inflation adjustment, and holiday correction are applied to:
Remove trends Stabilize variance
Improve stationarity
Example: Differencing removes upward sales trends.
5(a) Exponential Smoothing Models
First-order (Simple) smoothing: Used for data without trend or seasonality.
Second-order smoothing: Handles trends using two smoothing equations.
These models are simple and efficient for short-term forecasts.
5(b) Generalized and Weighted Least Squares
GLS and WLS address heteroscedasticity and autocorrelation, unlike ordinary least squares.
They assign different weights to observations, improving estimation accuracy.
6(a) AR and MA Models
AR models use past values MA models use past errors
ARMA combines both
They capture serial correlation patterns effectively.
6(b) Role of ACF and PACF
ACF identifies MA terms PACF identifies AR terms
They help in model selection and adequacy checking.
7(a) Multivariate Time Series Models
Multivariate models analyze interrelated time series simultaneously.
Advantages: Captures interactions
Improves forecasting accuracy Univariate models analyze variables independently.
7(b) Model Selection Criteria
Common criteria include:
AIC BIC
MAPE RMSE
Lower values indicate better model performance.
