Business Forecasting Topic 9 Flashcards
non stationary
trend
- ACF dying out extremely slowly -> when data manifests a trend/drift observations tend to be on same side of mean and therefore large autocorrelations still occur at relatively long time lags
differencing series to achieve stationarity
differences normally from random series = not constant
sure differences are stationary = model them using one of standard box Jenkins model
first difference
differences in sales between successive months
observation lost at start of series
random walk model
ARIMA (0,1,0)
first differences of random walk series follow white noise process
ACF of random walk model
ACF - indicates non stationarity
take differences = new series is stationary characterised by white noise process -> though strictly such a process requires normal distribution of differences
ARIMA (1,1,0)
first differences follow first order autoregressive process
difference between observation for period 2 and 3 is function of difference between periods 1 and 2
ARIMA (0,1,1)
first differences followed by a first order moving average model
backshift operator (B)
placing in front of observation = has effect of lagging it by 1 period
BY1 = Yt-1
over differencing
more differences than required = should avoid
use of first differences in time series analysis = common (sometimes second)
artificially introduce moving average terms into model of differentiated time series = cause unnecessary complications
relationship with exponential smoothing models
shown forecasts obtained from exponential smoothing methods are same as those obtained from certain ARIMA models
Simple exponential smoothing forecasts with something constant of α -> ARIMA (0,1,1) forecasts where theta 1 = (1 - α)
holts method = ARIMA (0,2,2)