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It is said that a time series is stationary if its mean, variance and auto-covariance are not dependent on time. Variables with means and variance that change over time, are known as non-stationary or unit-root variables (Glynn, Perera, & Verma, 2007). The unit-root test is particularly important in the present study, as it determines the type of structural-break method to use, in order to identify the date of the change in the time series. By including the trend in non-trending data, some of this change may be absorbed, producing spurious results (Piehl, Cooper, Braga, & Kennedy, 2003). Therefore, before testing for a structural break, it is essential to determine whether the data is stationary, with or without trend.

In this section, two sets of tests are applied. The first, which treats the unit root as the null hypothesis, includes both the Augmented Dickey-Fuller (ADF) and the Phillips and Perron (PP) unit root tests, while the second treats stationarity as the null hypothesis. This set includes The Kwiatkowski–Phillips–Schmidt–Shin (KPSS) test, which is used in this thesis.

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Augmented Dickey-Fuller (ADF) and Phillips and Perron (PP) tests

The first to be applied are the ADF and PP tests. The PP statistics are non-parametric versions of the ADF statistics, so their asymptotic distribution remains unaffected by serial correlation (Bartholdy, Peare, & Willett, 2000). Two versions of each test are applied, where: ADF models: ∆𝑦_𝑡 = 𝑢 + 𝛼𝑦_𝑡−1+ ∑𝑙 𝑐_𝑖 𝑖=1 ∆𝑦𝑡−𝑖+ 𝜀𝑡 5.1 ∆𝑦𝑡 = 𝑢 + 𝛽𝑡 + 𝛼𝑦𝑡−1+ ∑𝑙𝑖=1𝑐𝑖∆𝑦𝑡−𝑖+ 𝜀𝑡 5.2 PP models: ∆𝑦_𝑡 = 𝑢 + 𝛼𝑦_𝑡−1+ 𝜀_𝑡 5.3 ∆𝑦_𝑡 = 𝑢 + 𝛽𝑡 + 𝑎𝑦_𝑡−1+ 𝜀_𝑡 5.4

In all, the null hypothesis is equivalent to:

H0: 𝛼 = 0 (i.e., the data has a unit root)

The alternative hypothesis is:

H1: 𝛼 < 0 (i.e., the data has no unit root)

where ∆ is the first-difference operator, 𝑦𝑡is the foreign investment flow series, t is the time trend, and l is the number of lags to ensure that the error term, 𝜀_𝑡 , is a white-noise disturbance and 𝑡 = 1 … , 𝑇 is the time period. Equations 5.1 and 5.3 include intercept(𝑢), while equations 5.2 and 5.4 include intercept (𝑢) and trend(𝑡).

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Table 5.2 shows the results for ADF and PP, for both the aggregated and disaggregated series, with intercept, and intercept and trend. For each test, columns 1 and 2 show the t- statistic value of the autoregressive coefficient (α), and column 3 shows the trend coefficient (β) (its t-statistic valueis reported in parentheses). The null hypothesis of the

unit root is rejected if the t-statistic for α is greater than the critical value (the critical values are provided in the footnote of Table 5.2). As expected, the results are mixed. The existence of a unit root is not rejected in any of the tests when only the intercept is included (Column 1 of each test). Although, when the trend (β) is included (Columns 3 of each test), the t-statistic values for the coefficient (α) are enhanced (Columns 2 of each test), the unit root hypothesis is only rejected for TFE and FDR under the ADF, and FDR and FPE under the PP test; however, it is only at the 10% level. All series (except FPD) show a significant positive trend at the 10% level or better, which supports the visual impression given by the graph in Figure 5.5.

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Table 5. 2: Augmented Dickey-Fuller (ADF) and Phillips-Perron (PP) Unit Root Test Results

test ADF PP

model Intercept Intercept and trend Intercept Intercept and trend

Coefficients α α β α α Β Total Foreign Investment TFI 1.1912 -1.66 0.0023* (1.9312) 0.4828 -1.88 0.0017* (1.8985) Total Foreign Equity TFE 0.3895 -3.20 0.0051***

(3.1910)

-0.278 -3.02 0.0043*** (2.7669) Total Foreign Debt TFD 1.2485 -1.31 0.0011*

(1.6859) 1.1108 -1.39 0.0011* (1.6859) Foreign Portfolio Equity FPE -0.888 -2.52 0.0091** (2.4304) -0.832 -3.24 0.0058*** (2.770) Foreign Direct Equity FDE 0.330 -1.95 0.0023**

(2.116)

0.0582 -2.16 0.0023** (2.218) Foreign Direct Debt FDD 1.3739 -1.25 0.00123**

(1.9976)

1.5121 -1.20 0.00123** (1.998) Foreign Portfolio Debt FPD 0.3220 -1.49 0.0011

(1.6283) 0.6405 -1.49 0.0011 (1.525) Foreign Loan FL -0.105 -1.50 0.00093* (1.65938) -0.105 -1.50 0.0009* (1.659) Foreign Derivative FDR -0.482 -3.24* 0.0140*** (3.225) -0.473 -3.23* 0.0118*** (3.336) Other Foreign Debt OFD 1.4097 -2.36 0.0058**

(2.567)

0.9716 -2.87 0.0052*** (3.0375) Note:

Critical value; ADF = -3.500, -2.8922, -2.583192, PP = -3.5006, -2.8922, -2.583192 with intercept only, and ADF= -4.058, -3.458, -3.155, PP = -4.0576, -3. 457, -3.154 with intercept and trend, at 1%, 5%, and 10% levels, respectively.

***, **, * significant at the 1%, 5%, and 10% levels respectively.

In the ADF tests, in order to select the optimal lag length (l), the t test criterion approach is used. This involves starting with a pre-determined upper bound l max. If the last included lag is significant,

l max is chosen. However, if l is not significant, it is incrementally reduced by one lag at a time until

the lags become significant. If no lags are significant, l is set at zero. The test is employed with l =11, which is (𝑁_𝑖× 12 100⁄ ), where 𝑁_𝑖 is the number of observations in each series. Also, a asymptotic critical value of approximately 5% is used to determine the significance of the t-statistic on the last lag (Perron, 1997).

In the PP tests, the Bartlett kernel estimation method is selected (default method), and to control the lag length, Andrew’s Bandwidth is used.

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There have been some criticisms of these two tests. For example, Kwiatkowski, Phillips, Schmidt, and Shin (1992) hold that the existence of a unit root is the null hypothesis of these tests, and in classical hypothesis testing, this null is accepted unless there are strong grounds for doing otherwise. Therefore, the ADF and PP tests are not regarded as being very powerful against the relevant alternative hypothesis. The mixed results, reported in Table 5.2 could reflect the problems identified by Perron (1989) and others. The ADF and PP tests have low power if the series is stationary with trend, and the existence of structural breaks in stationary data, which is expected to be the case for the foreign investment inflow series, can sometimes make a stationary time series appear non- stationary.

In contrast, the second set of tests for unit root, which includes the Kwiatkowski–Phillips– Schmidt–Shin (KPSS) test used in this thesis, is based on the null hypothesis that a series is stationary. Such tests are said to have more power than the ADF and PP tests to accept the stationarity with trend. Accordingly, the KPSS test is used to supplement the first set of tests.

Kwiatkowski–Phillips–Schmidt–Shin (KPSS) test

This set is usually used to test the null hypothesis of stationarity, versus non-stationarity, around the mean or trend (see Lee & Lee, 2012). The KPSS takes the following forms:

𝑌𝑡= 𝑢 + 𝜑𝑡+ 𝜀𝑡 5.5

𝑌𝑡= 𝑢 + 𝛽𝑡 + 𝜑𝑡+ 𝜀𝑡 5.6 Where 𝜀 is stationary and a random walk, i.e.:

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𝜑𝑡 = 𝜑𝑡−1+ 𝜔𝑡 _5.7

The null hypothesis is H0 = 𝜎𝜔2 = 0, which implies that 𝜑𝑡 is constant.

Table 5.3 shows the results of the KPSS test. The null hypothesis of stationarity cannot be rejected if the t-statistic for 𝜑 is less than the critical value (the critical limits are shown in the footnote of Table 5.3). For intercept only (Column 1), the null hypothesis of stationarity is rejected; however, when the trend is included (Columns 2 and 3) as expected, the foreign investment inflow series appear to be stationary around the deterministic trend, with a significant positive trend.

The evidence obtained from the ADF, PP, and KPSS tests, along with the visual evidence provided in Figure 5.5, suggests that the data has trend. The mixed results concerning stationarity hint at the possibility of the series having one or more structural break. Therefore, in the following section, structural-breaks tests with trending data are used to investigate whether a break exists in Australia’s foreign investment components, around the date on which A-IFRS was introduced.

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Table 5. 3: Kwiatkowski–Phillips–Schmidt–Shin (KPSS)Unit Root Test Results

Model intercept Intercept and trend

Coefficients α α Β

Total Foreign Investment TFI 1.161 0.14 0.0274***

(43.90)

Total Foreign Equity TFE 1.243 0.11 0.0278***

(48.97)

Total Foreign Debt TFD 0.777 0.20 0.0271***

(37.591)

Foreign Portfolio Equity FPE 0.591 0.08 0.035***

(50.22)

Foreign Direct Equity FDE 2.959 0.13 0.023***

(35.76)

Foreign Direct Debt FDD 0.533 0.21 0.0258***

(22.032)

Foreign Portfolio Debt FPD 0.930 0.20 0.0272***

(37.868)

Foreign Loan FL 1.868 0.159 0.0185***

(17.510)

Foreign Derivative FDR 0.615 0.10 0.0429***

(38.172)

Other Foreign Debt OFD 0.794 0.155 0.0318***

(65.181)

Critical value: 0.7390, 0.4630, 0.3470 with intercept only, and 0.216, 0.146, 0.119 with intercept and trend, at 1%, 5%, and 10% levels, respectively.