Time Series Econometrics Using Microfit 5 0 Pdf WORK

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Although the ARDL cointegration method is not sensitive to the order of integration of the time series, nevertheless it is essential to conduct a unit root test to ensure that none of the variables are ; otherwise the computed F-statistics, as produced by Pesaran et al. [5], can no longer be valid. Two unit root tests are used in this paper, the augmented Dickey-Fuller (ADF) test and the Kwiatkowski-Phillips-Schmidt-Shin (KPSS) test. Three versions of the Augmented Dickey-Fuller (ADF) are conducted. One version allows for an intercept, a second allows for an intercept and a deterministic trend, and a third version excludes the intercept and the deterministic trend. For the KPSS test, two versions are used; one version allows for an intercept, and a second allows for an intercept and a deterministic trend. (The KPSS is a test of the null hypothesis that the series is stationary around a deterministic trend. The series is expressed as the sum of a deterministic trend, a random walk, and a stationary error, and the test is the Lagrange multiplier test of the hypothesis that the random walk has zero variance [35].)

The bounds testing approach to cointegration is conducted in two steps. The first step involves testing the existence of a long-run relationship between remittances and GDP using two-test statistics: an F-test for the joint significance of the coefficients of the lagged level variables (H0: and a t-test for the statistical significance of the coefficient on the lagged level of the dependent variable (H0: = 0). Pesaran et al. [5] considered that the F-statistic does not follow the standard F-distribution and hence they provided lower and upper bound critical values. The lower bound critical values assume that all variables are I(0) while the upper bound values assume that they are . Similar to the F-statistic, the t-statistic does not follow the standard t-distribution and Pesaran et al. [5] also provided their lower and upper bound critical values. Cointegration between the variables of interest is established if the F- and t-statistics exceed the upper bound critical values. A note worth mentioning is that the F-statistic is affected by two factors, the lag length of the first-order differenced variables in (3) and the inclusion of a time trend. The decision about these two factors will be discussed in the next section. All tests and estimation are conducted using Microfit 5 [37].

Augmented Dickey Fuller test (ADF Test) is a common statistical test used to test whether a given Time series is stationary or not. It is one of the most commonly used statistical test when it comes to analyzing the stationary of a series.1. IntroductionIn ARIMA time series forecasting, the first step is to determine the number of differencing required to make the series stationary.

As see earlier, the null hypothesis of the test is the presence of unit root, that is, the series is non-stationary.# Setup and Import datafrom statsmodels.tsa.stattools import adfullerimport pandas as pdimport numpy as np%matplotlib inlineurl = ' 'df = pd.read_csv(url, parse_dates=['date'], index_col='date')series = df.loc[:, 'value'].valuesdf.plot(figsize=(14,8), legend=None, title='a10 - Drug Sales Series');The packages and the data is loaded, we have everything needed to perform the test using adfuller().An optional argument the adfuller() accepts is the number of lags you want to consider while performing the OLS regression.By default, this value is 12*(nobs/100)^{1/4}, where nobs is the number of observations in the series. But, optionally you can specify either the maximum number of lags with maxlags parameter or let the algorithm compute the optimal number iteratively.if(typeof ez_ad_units!='undefined'){ez_ad_units.push([[300,250],'machinelearningplus_com-large-mobile-banner-1','ezslot_10',612,'0','0'])};__ez_fad_position('div-gpt-ad-machinelearningplus_com-large-mobile-banner-1-0');This can be done by setting the autolag='AIC'. By doing so, the adfuller will choose a the number of lags that yields the lowest AIC. This is usually a good option to follow.# ADF Testresult = adfuller(series, autolag='AIC')print(f'ADF Statistic: {result[0]}')print(f'n_lags: {result[1]}')print(f'p-value: {result[1]}')for key, value in result[4].items(): print('Critial Values:') print(f' {key}, {value}') Result:ADF Statistic: 3.1451856893067296n_lags: 1.0p-value: 1.0Critial Values: 1%, -3.465620397124192Critial Values: 5%, -2.8770397560752436Critial Values: 10%, -2.5750324547306476The p-value is obtained is greater than significance level of 0.05 and the ADF statistic is higher than any of the critical values.

Figure 6 displays the estimated pointwise elasticities for Denmark and Sweden against income and time using the different scaling factors. Like Fig. 3 for the quadratic case, Fig. 6 clearly shows that for the cubic case, the elasticity estimates are not unit dependent (both when plotted against income and time). For both Denmark and Sweden, the estimated pointwise elasticities are positive and significant at low levels of income but gradually fall, becoming insignificant the closer to the estimated first turning point, where the elasticity would be zero. Thereafter, as income increases, the estimated elasticities continue to fall, gradually becoming more negative and significant. However, Denmark then follows a different path to that of Sweden. For Denmark, the estimated elasticities flatten and do not reach the second turning point, given it is outside of the data range, whereas for Sweden, the estimated elasticities start to rise again, becoming around zero at the estimated second turning point and then continue to rise. As for the charts against time in the second column of Fig. 6, these show slightly different patterns but still reflect the situation in the first column. Again, it is interesting to focus on the illustrative estimates for Denmark presented in Fig. 6, since the plots against both income and time show that the cubic or N-shaped specification is not appropriate. For there to be an N-shaped pattern, the elasticity should have at least some positive values after the second turning point when plotted against income (and close to the end of the sample when plotted against time). However, this is clearly not the case for Denmark in Fig. 6, which is in line with the finding of the second turning point to be outside of the sample range for Denmark. Nonetheless, this is the case for Sweden in Fig. 6, which would be expected given both estimated turning points are within the data sample range, and Fig. 6, therefore, suggests that an estimated N-shaped EKC might be appropriate for Sweden.

Finally, for completeness, Fig. 9 displays the estimated pointwise elasticities for both countries against income and time using the different scaling factors and again shows that the elasticity estimates are not unit dependent. Since the pointwise elasticity is insignificant for both country cases, it confirms what has been suggested above in terms of the insignificance of the leading term and the turning points: the quartic specification is not the appropriate representation of the EKC relationship for either country.

This paper has explored important issues around estimating logarithmic EKCs using various orders of polynomial specifications in detail. It highlights some of the common pitfalls but also develops a modelling strategy that should ensure a consistent approach for researchers investigating logarithmic EKCs. Footnote 25 That said, this paper focuses very much on the one type of specification, albeit an extremely popular type, and when undertaking such modelling, it is vital that the correct and appropriate econometric estimation and testing techniques are employed to the highest standard and considered alongside the modelling strategy suggested above. Moreover, future research should consider how the non-linear polynomial specifications considered in this paper could be used, or compared, with econometric non-linear modelling methods as discussed in Lieb (2003), Dinda (2004), and Kijima et al. (2010), inter alia. These include the structural time series method (Harvey 1989); time-varying coefficient cointegration (Park and Hahn 1999); quantile cointegration regression (Xiao 2009); and the multiplicative indicator saturation approach (Ericsson 2012; Castle and Hendry 2019).

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