We use linear models primarily to analyse cross-sectional data; i.e. data collected at one specific point in time across several observations. We can also use such models with time series data, but need to be cautious of issues such as serial correlation.
A neural network is a computational system that creates predictions based on existing data. Let us train and test a neural network using the neuralnet library in R.
Serial correlation (also known as autocorrelation) is a violation of the Ordinary Least Squares assumption that all observations of the error term in a dataset are uncorrelated. In a model with serial correlation, the current value of the error term is a function of the one immediately previous to it:
et = ρe(t-1) + ut where e = error term of equation in question; ρ = first-order autocorrelation coefficient; u = classical (not serially correlated error term)
When we refer to a time series as stationary, we mean to say that its mean, variance and autocorrelation are all consistent over time. Cointegration, on the other hand, is when we have two time series that are non-stationary, but a linear combination of them results in a stationary time series. So, why is the concept of stationarity important? Well, a large purpose of time series modelling is to be able to predict future values from current data.