The values of a series of data at a particular point in time is highly correlated with the values that precede and succeed them. In simple term, observations are not independent. This can be checked by using Durbin-Watson statistics as follow:

We can model the autocorrelation if present in the time-series by using Autoregressive Integrated Moving Average (ARIMA) models.

First - Order Autocorrelation Model (association between two consecutive values in the series)

Y_i = A₀ + A₁Y_i-1 + Ɛ_i

Second - Order Autocorrelation Model (association between values that are two periods apart)

Y_i = A₀ + A₁Y_i-1 + A₂Y_i-2+ Ɛ_i

p^th Order Autocorrelation Model (association between values that are pth periods apart)

Y_i = A₀ + A₁Y_i-1 + A₂Y_i-2+ ...A_pY_i-p +Ɛ_i

Y_i = Observed value of time-series at time i
Y_i-1 = Observed value of time-series at time i – 1
A₀ = Fixed least-square parameter
A₁, A₂, A_p = Autoregressive parameters to be estimated using least-square regression.
Ɛ_i = Random error at time i

Forecast = Ŷ_{n + j} = A₀ + A₁ Ŷ_{n + j -1} + A₂ Ŷ_{n + j -2} + … A_p Ŷ_{n + j -p}

Notes:

It is important to select the order of autocorrelation in the Auto-Regressive models. You can use the t-test to test for the significance of respective order of autocorrelation. In Eastman Kodak revenue, third order auto-regressive model is not significant and hence, second order model is fitted to the time series data and same is used to forecast the value for Year = 2000 and 2001.

You must be equally concern with selecting the high order model as it requires estimation of high order parameters. This may cause problem especially when the number of observations are less.