Forecasting Flashcards
What does ARIMA stand for
Autoregressive Integrated Moving Average
When is an ARIMA Process stationary
When d=0
How can we transform an ARIMA process where d=k k not zero to be stationary
Apply k differences
What are the three/four key steps in the box jenkins methodology
- preliminary analysis
- identification and estimation
- model diagnostics
(4 forecasting)
What are the steps in the box jenkins method under preliminary analysis?
Plotting the time series
If the variance isnt constant using log or box cox transform to stabilise
Plot ACF - take differences until reaching stationarity (avoid unnecessary differencing)
Study ACF and PACF to determine max lags for ARMA model
What are the steps in the box jenkins method under identification and estimation?
Identify p and q with criterion like AIC, AICc or BIC
Once a model is selected estimate the parameters using ex: maximum likelihood
Examine fitted coefficients and their SErrors and see if some of them can be set to zero
What are the steps in the box jenkins method under model diagnostics?
Check is residuals are behaving like white noise
Plot ACF and qq norm graph and histogram of residuals and test for normality using shapiro wilks
Perform ljung box pierce test
What is our aim when forecasting?
Find a linear combination of observed Xn….X1 that forecasts X n+h with minimum mean squared error where Xt is a stationary time series
How do we find the parameters/ weights a in the best linear predictor formula
Minimising the mean squared error
How do we minimise the mean squared error
Find the derivative of it wrt each aj and set these derivatives equal to zero - will have n+1 equations to solve for n+1 parameters
What is function for forecasting in R
sarima.for
What is the layout of function sarima.for in R
Sarima.for(x, n.ahead=-,p=-,d=-,q=-,plot.all=TRUE)
