AutoRegressive Integrated Moving Average 
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ARIMA 
Summary of AutoRegressive Integrated Moving Average. Abstract 
© / ™Box and Jenkins 
Although nobody can really look into the future, modern statistical methods, econometric models and business intelligence software go a long way in helping businesses forecast and estimate what is going to happen in the future.
ARIMA stands for AutoRegressive Integrated Moving Average.
The ARIMA Time Series Analysis
uses lags and shifts in the historical data to uncover patterns (e.g.
moving averages, seasonality) and predict the future. The ARIMA model was
first developed in the late 60s but was systemized by Box and Jenkins in
1976. A can be more complex to use than other statistical forecasting
techniques, although when implemented properly can be quite powerful and
flexible.
A is a method for determining two
things:
1. How much of the past should be used to predict the next observation
(length of weights)
and
2. The values of the weights.
For example y(t)= 1/3 * y(t3) + 1/3 * y(t2) + 1/3 * y(t1) is an ARIMA
model; another one is y(t)= 1/6 * y(t3) + 4/6 * y(t2) + 1/6 *
y(t1)
Thus the correct A model requires identification of the right number
of lags and the coefficients that should be used.
A model identification uses autoregressions to IDENTIFY the underling
model.
Care must be taken to robustly IDENTIFY and ESTIMATE PARAMETERS as
outliers (pulses, level shifts , local time trends ) can wreak havoc.
Book: Alan Pankratz  Forecasting with Univariate Box Jenkins Models : Concepts and Cases
Book: Jeffrey Wooldridge  Introductory Econometrics: A Modern Approach
💡  Here you can learn more and discuss statistical forecasting and ARIMA. 
Compare with ARIMA: Regression Analysis  Dynamic Regression  Exponential Smoothing
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