#### Autoregressive model - Wikipedia

https://en.wikipedia.org/wiki/Autoregressive_forecasting

Since the AR model is a special case of the vector autoregressive model, the computation of the impulse response in vector autoregression#impulse response applies here. n-step-ahead forecasting. Once the parameters of the autoregression = + ∑ = − +

#### Autoregression Models for Time Series Forecasting With Python

https://machinelearningmastery.com/autoregression-models-time-series-forecasting-python/

Autoregression is a time series model that uses observations from previous time steps as input to a regression equation to predict the value at the next time step. It is a very simple idea that can result in accurate forecasts on a range of time series problems. In this tutorial, you will discover ...

#### Introduction to Time Series Regression and Forecasting

http://www.ssc.upenn.edu/~fdiebold/Teaching104/Ch14_slides.pdf

A natural starting point for a forecasting model is to use past values of Y (that is, Y t–1, Y t–2,…) to forecast Y t. An autoregression is a regression model in which Y t is regressed against its own lagged values. The number of lags used as regressors is called the order of the autoregression. o In a first order autoregression, Y

#### Time series Forecasting — ARIMA models

https://towardsdatascience.com/time-series-forecasting-arima-models-7f221e9eee06

P = Periods to lag for eg: (if P= 3 then we will use the three previous periods of our time series in the autoregressive portion of the calculation) P helps adjust the line that is being fitted to forecast the series. Purely autoregressive models resemble a linear regression where the predictive variables are P number of previous periods

#### 8.3 Autoregressive models | Forecasting: Principles and ...

https://otexts.com/fpp2/AR.html

8.3 Autoregressive models. In a multiple regression model, we forecast the variable of interest using a linear combination of predictors. In an autoregression model, we forecast the variable of interest using a linear combination of past values of the variable. The term autoregression indicates that it is a regression of the variable against ...

#### ARIMA models for time series forecasting - Duke University

https://people.duke.edu/~rnau/411arim.htm

ARIMA(1,0,0) = first-order autoregressive model: if the series is stationary and autocorrelated, perhaps it can be predicted as a multiple of its own previous value, plus a constant. The forecasting equation in this case is . Ŷ t = μ + ϕ 1 Y t-1 …which is Y regressed on itself lagged by one period. This is an “ARIMA(1,0,0)+constant” model.