AR(1) Process Simulation Tool

Background

This tool simulates a stochastic process that is autoregressive of order 1 or AR(1). A random variable $X_t$ that follows an AR(1) process can be written as: $$X_t = (1-\rho) \mu + \rho X_{t-1} + \epsilon_t,$$ where $\mu$ is the unconditional mean of the process, $\rho$ is the coefficient of autocorrelation, and $\epsilon_t$ is a white noise (WN) process with standard deviation $\sigma_{\epsilon}$. The coefficient of autocorrelation $\rho$ determines the extent to which the previous — or lagged— value of $X$ affects the current value.

Instructions

Choose the values of $\mu$, $\rho$, $\sigma_{\epsilon}$, and $X_0$ for the process that you want to simulate. Then choose the number of periods for the simulation and select which type of simulation that you want to perform:

Stochastic simulation: a new random value for the white noise process $\epsilon_t$ will be drawn for each period.
Impulse response: $\epsilon_t$ will be set to $\sigma_{\epsilon}$ in period 1 and to 0 in all subsequent periods.

Use the dropdown menu in the upper-right corner of each plot to download the image in png format. Click the "Download csv" button to download the data in both figures in a single csv file.