State whether the following sentences are true or false and provide a proper justification for each of the answers.

(a.) To determine the appropriate lag length of an ADL model describing the relationship between two time series, y and x, we should seek to minimize the sum of squared residuals.

(b.) If the data series y has a Partial Autocorrelation Function, it implies the data is stationary: However, if y has an Autocorrelation Function, the data is non-stationary.

(c.) Exponential smoothing models are preferred to ARIMA models if the data is cross-sectional.

(d.) OLS applied to a VAR of an appropriate lag length may give unbiased estimates of the relationships between two or more time series variables, whether or not the variables are cointegrated.

(e.) Where two series are cointegrated, ARIMA allows the estimation of the error correction model.

please answer only if you can give proper justification for each of the parts.