Appendix 2: Time Series Properties of the Data | RDP 9312: A Re-examination of the Determinants of Australia's Imports

RDP 9312: A Re-examination of the Determinants of Australia's Imports Appendix 2: Time Series Properties of the Data

Jacqueline Dwyer and Christopher Kent

December 1993

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Each of the series used in estimating the excess demand for imports was tested for non-stationarity using the Augmented Dickey Fuller (ADF) test (Said and Fuller 1984). The null hypothesis is the existence of non-stationarity.

Four lags of the differenced series were included in the ADF test. Lagrange multiplier tests were conducted to test for first, and joint first to fourth order autocorrelation. The test statistic was taken from the specification of the ADF test which was free from autocorrelation and had the smallest number of lags.

The results reported in Table A2.1 are for the tests in which a constant is included. For the Z_t test, five lags of the covariance were included.

Table A2.1: Results of Unit Root Tests
Imports:	Order	ADF	Z_t
Aggregate^*	level 1st difference	−1.35 −5.39	−0.51 −7.43
Consumption	level 1st difference	−1.24 −6.58	−1.32 −6.72
Intermediate	level 1st difference	−1.39 −6.95	−1.38 −7.17
Capital	level 1st difference	−2.28 −3.15	−2.50 −6.77
Relative Price of Imports:
Aggregate^*	level 1st difference	−1.72 −7.77	−2.06 −7.93
Aggregate Landed^*	level 1st difference	−1.36 −7.78	2.39 −7.95
Consumption	level 1st difference	−1.58 −7.64	−1.90 −7.84
Intermediate	level 1st difference	−1.25 −6.52	−1.32 −6.63
Capital	level 1st difference	−2.30 −3.23	−1.97 −6.96
Activity:
Real GNE^*	level 1st difference	−0.40 −7.44	−0.48 −7.57
Protection:
Effective rate of assistance^*	level 1st difference	0.38 −2.10	2.32 −2.15
Note: Series denoted by * are tested for stationarity during the period from the September quarter 1974 to the March quarter 1993. All other series are tested during the period from the September quarter 1979 to the March quarter 1993.

In Table A2.1, the results of stationarity testing of both the log level and log difference of the series are reported. All series posses one unit root, with the exception of the effective rate of assistance which, for the period of estimation, may have two unit roots. However, this variable is not determined by a stochastic process; it is set by policy and movements in it can be interpreted as a shift in the constant in each period in which it exhibits change. Its time series properties do not compromise the cointegrating relationship observed between imports and its explanators.

The critical values are taken from Fuller (1976):

−3.51 at the 1 per cent level;
−2.89 at the 5 per cent level; and
−2.58 at the 10 per cent level.

With the exception of the effective rate of assistance, the null hypothesis of non-stationarity is accepted at the 10 per cent level for log levels and rejected at the 5 per cent level for first differences. (In fact, non-stationarity of first differences is rejected at the 1 per cent level for most series.)