Welcome to our presentation

Welcome to our presentation. Presented by : Members of group c Rumi, Rezwan, Sazib, Tawhid, Sharif Department of statistics Pabna University of science and Technology.

The ARIMA model (AutoRegressive Integrated Moving Average) is a popular statistical method for analyzing and forecasting time series data. ARIMA(p,d,q) Where, p=number of autoregressive terms d=number of differencing q=number of moving average terms Now ARIMA(p,0,q)=ARMA(p,q) ARIMA(p,0,0)=AR(p) ARIMA(0,0,q)=MA(q).

Autoregressive & Moving Average Model. Autoregressive Model:An AutoRegressive (AR) model is a type of statistical model used for time series data, where the current value of the series depends on its previous values. In simple terms, it predicts future values based on past observations. Moving Average Model:A Moving Average (MA) model is a statistical model used in time series analysis, where the current value of the series depends on the past error terms (or "shocks"). It helps smooth out fluctuations in the data by averaging over a set number of previous observations..

Impulse Response Function (IRF). The Impulse Response Function (IRF) in time series analysis examines the impact of a shock to one variable on current and future values of variables in a dynamic system. It is especially important in Vector Autoregression (VAR) models, which are widely used for analyzing multiple time series that may influence each other over time. Let’s go through an example of an Impulse Response Function (IRF) analysis involving GDP and interest rates. In this example, we want to see how a shock in interest rates (like a sudden increase) affects GDP over time..

AutoCorrelation Function & Partial AutoCorrelation Function.

Overview of our presentation. Concept of VAR model with Example Concept of SVAR model with Example Advantages of VAR and SVAR model.

Defination of VAR Model. A VAR (Vector Autoregressive) model is a system of equations where each variable in the model is explained by its own past values (autoregressive part) and the past values of all other variables in the system. It is called "vector" because it involves multiple variables, and "autoregressive" because each variable depends on its previous values..

Defination of SVAR model. A SVAR model stands for Structural Vector Autoregressive model. It is an extension of the traditional VAR (Vector Autoregressive) model, which is used to capture the interrelationships between multiple time series. The main difference between a VAR and SVAR model lies in the identification of the structural relationships between the variables..

Example of SVAR MOdel. Monetary Policy Analysis: In macroeconomics, an SVAR model might be used to study how a monetary policy shock (like a change in interest rates) affects other variables like inflation and output (GDP). By adding identifying restrictions, an SVAR can estimate the immediate (contemporaneous) impact of monetary policy and isolate the structural shocks to inflation or output. Identifying Demand and Supply Shocks: In a model involving output and inflation, the SVAR can be used to distinguish between demand-side shocks (e.g., a sudden increase in consumer spending) and supply-side shocks (e.g., a supply chain disruption.

VAR Advantages: Flexibility and simplicity. Good for modeling short-term dynamic relationships. Suitable for forecasting and analyzing interdependencies. No need for prior structural assumptions. SVAR Advantages Provides structural interpretation and causal inference. More appropriate for policy analysis and understanding shocks. Integrates economic theory into the model. Helps in distinguishing between different types of shocks (e.g., demand vs. supply)..

Structural Analysis. The general var(p) model has many parameters and they may be difficult to interpret due to complex interactions and feedback between the variables in the model. As a result the dynamic properties of a var(p) are often summarized using various types of structural analysis..

The three main types of structural analysis summaries are:.

Out lines. Definition with Example. Test procedure of Granger Causality.

Definition of Granger Causality with Example. Definition: According to the Granger(1969),y is said to “Granger cause m if and only if m is better predicted by using the past values of y than by not doing so with the past values of m being used in either case, In short , if a scaler y can help to forecast another scaler m, then we say that y Granger causes If y causes m and m doesn’t cause y, it is said that unidirectional causality exist from y to m. If y does not cause m and m does not cause y, then m and y are statistical independent. If y causes m and m causes y, it is said that feedback exists between m and y. Essentially Granger’s definition of causality is framed in terms of predictability. In the econometrics, Granger causality is used for testing exogencity. Example: GDP is effected by Inflation or other things , we don’t before estimating F value. After estimating the F-test ,then we can decide which is Granger causality ..

Test procedure of Granger Causality. Data Preparation: Time Series Data: Obtain the two time series data sets you want to analyze, typically denoted as Xt and Yt. Stationarity Check: Ensure that both time series are stationary. This often involves differencing the data if they are not already stationary. Non-stationary data can lead to spurious results. Lag Length Selection: Determine Optimal Lag Length: Use criteria such as the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), or the Hannan-Quinn criterion (HQC) to determine the appropriate number of lags to include in the model. This step is crucial as the choice of lag length can affect the results of the test..

Forecast Error Variance (FEV) in Time Series Analysis.

Time Series. Definition: Forecast Error Variance (FEV) refers to the variance in the error of predictions or forecasts over time. It quantifies the uncertainty or deviation in forecasted values from actual outcomes..

Use Case. Economic and Financial Forecasting Weather and Climate Prediction Supply Chain and Inventory Management Healthcare and Epidemiology Energy and Utilities Management Marketing and Sales Forecasting.

Limitations. 1. Sensitivity to Model Choice 2. Overfitting Risk 3. Limited to Quantitative Data 4. Time Dependency 5. Assumes Stationarity 6. Data Quality Sensitivity.