## ADF Test: Augmented Dickey Fuller Equation

The Augmented Dickey Fuller or ADF Test of stationarity is a unit root based test. It attempts to overcome the shortcomings of the original Dickey Fuller test. Researchers often observed…

## Cointegration: Meaning, Tests and Models

Cointegration refers to the situation where the variables have a long-run or equilibrium relationship. Such variables move together over time and can be said to have a similar wavelength or…

## Order of Integration of a time series

If a non-stationary time series has to be differenced “d” times to make it stationary, that time series is integrated of order "d". In other words, the order of integration…

## Dickey Fuller Test of Stationarity

The Dickey Fuller Test is a unit root based test of stationarity. The unit root based tests focus on the coefficient associated with the first lag of the time series…

## Autocorrelation function and Stationarity

The ACF or Autocorrelation Function is one of the most widely used methods to check for stationarity of a time series. Moreover, it also gives valuable insights into the autoregressive…

## Random Walk Model and Stationarity

The Random Walk Model is an example of a non-stationary time series. This model is often used to discuss and illustrate the concepts of stationarity, unit root process and order…

## Stationarity and Stationary Time Series

A time series is said to be stationary if its characteristics do not change with time. Moreover, a stationary time series can be identified as strictly stationary or weak stationary.…

## VAR in R: Estimation, Goodness and IRFs

Vector Autoregression or VAR can be estimated using several packages. We will use the "vars" and "tsDyn" packages to illustrate the application of VAR in R. In addition, we will…

## ARIMA and SARIMA in Rstudio

There are several packages available for estimating the ARIMA and SARIMA in Rstudio. Autoregressive Integrated Moving Average (ARIMA) and Seasonal Autoregressive Integrated Moving Average (SARIMA) models are often used for…

## Interpreting ACF and PACF plots

Autocorrelation Function (ACF) and Partial Autocorrelation Function (PACF) can provide valuable insights into the behaviour of time series data. They are often used to decide the number of Autoregressive (AR)…

## Seasonality and Seasonal-ARIMA models

Seasonality, sometimes referred to as seasonal variation, is common in economic time series. The time series variables may change in a cyclical pattern with time. This cyclical pattern is termed…

## ARIMA Model Estimation and Model Selection

Autoregressive Integrated Moving Average (ARIMA) models are often used for forecasting purposes. These models for time series data have been observed to provide accurate forecasts. Additionally, these models allow dynamic…

## VECM Estimation and Interpretation

The Vector Error Correction Mechanism (VECM) is estimated in the presence of cointegration among the system of variables. It allows us to estimate short-run as well as long-run coefficients. Using…

## Vector Error Correction (VECM) and VAR: Theory

Vector Error Correction Mechanism (VECM) models are a special application of VAR or Vector Autoregressive Models. The specification of VECM models involves the introduction of error correction terms into the…

## Impulse Response Functions after VAR and VECM

Impulse Response Functions or IRFs are used to study the effects of shocks or impulses in a VAR or VECM system. It traces out one unit or one standard deviation…

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