#### Özet

Testing the Linearity of Macroeconomic Time Series of Turkey

**1. ****Introduction**

There is a growing interest in nonlinear models for projections on economic relations and financial econometrics. Developments of the last thirty years in both linear and nonlinear models, as well as robust tests developed and introduced into literature in the last ten years, have made empirical studies more important.

According to Enders (2010), a significant number of economic theory’s time series variables can display nonlinear behaviors. However, linear models are used more than nonlinear models in empirical studies. The major reason for this is that it is easier both to implement linear models and to interpret their results.

Beyond linear impact area, there is an infinite number of nonlinear forms yet to be discovered. The first efforts in the analysis of nonlinear time series are concentrated on various nonlinear parametric forms (Fan and Yao, 15). In econometrics literature, the interest shown in nonlinear models has steadily increased for decades, especially with the bilinear model proposed by Granger and Andersen (1978) and the Threshold Autoregressive (TAR) model introduced by Tong and Lim (1980) and Tong alone (1983). The development of the Self-Exciting Threshold Autoregressive (SETAR) model, the Logistic STAR (LSTAR) model and the Exponential STAR (ESTAR) model have led to an increase in the use of nonlinear structures in empirical studies. Various nonlinear unit root and cointegration tests based on these models have been introduced into literature, and the execution of empirical studies that focus on nonlinear relations has increased.

The major studies in literature that examine the linearity and nonlinearity of macroeconomic series in literature can be summarized as follows: Teräsvirta, Van Dijk ve Medeiros (2005), Baillie ve Kapetanios (2007), Yoon (2009), Yoon (2010a), Yoon (2010b), Chen (2011), and Yavuz and Yılancı (2012).

**2. ****Methodology**

Various tests have been introduced into literature to test the linearity of the series. The major tests are as follows: McLeod and Li (1983), Keenan (1985), Tsay (1986), and Lee vd. (1993). Although these tests examine the linearity of series, they do not take into consideration their stationarity, and in the case of nonstationarity, they lose power. However, the linearity test introduced into literature by Harvey vd. (2008), hereafter referred to as HLX, is a test that can be used even at times when the stationarity of the series is uncertain.

The linearity test introduced by Harvey and Leybourne (2007) into literature can test the linearity of a series examined without making an assumption about the stationarity status of a series. Although the test introduced by HLX into literature displays similar characteristics, it has better finite sample size and power in comparison to the test in question.

The HLX test is applied simply by calculating the weighted mean of two different linearity tests. The first of these tests, , examines the linearity of the series based on the assumption that the series examined is stationary, whereas the second test, , examines linearity based on the assumption that the series has a unit root. The HLX test statistics obtained by the weighted mean of these two statistics in question is distributed as chi-square with two degrees of freedom.

**3. ****Results and Discussion**

The variables of this study, which aims to test the linearity of macroeconomic data of Turkey, are based on monthly frequency, and the beginning and ending dates are different due to insufficient data. The unemployment rates downloaded from the IMF databank are the monthly unemployment rate (UR), number of unemployed people (UP), and number of people employed (EP) for the period of January 2005–May 2015. The industrial production index (IPI) obtained from the same source is for the period of January 1985–June 2015, the Central Bank policy interest rate (INTEREST RATE) is for the period of October 1999–July 2015, and the import and export volume indexes (IVI and EVI) are for the period of January 1982–June 2015. The M3 money supply obtained from the OECD databank is for the period of January 2005–July 2015.

The HLX proposed using the ADF test as the unit root test and the Harris vd. (2003) (HML) test as the stationarity test. The ADF and HML tests were used for this study following Harvey’s proposal. When the test statistics are examined, the UR, UP, EP, M3, and IVI variables are linear, whereas the other variables included in the analysis are nonlinear.

The study by Yoon (2009) showed that the outliers are influential on the HLX linearity tests. The outliers were no longer present in the nonlinear UR series, whereas outliers were found to be present in the IPI, INTEREST RATE, and EVI variables. The analyses showed that the underlying reason for nonlinearity in INTEREST RATE is not outliers. Deviation from targeted inflation and output deficit could be the reasons for the nonlinearity found in interest rates whose source is not the outliers in the series. It is also worth mentioning that although the unemployment rate is linear, the number of people employed is nonlinear. The asymmetrical harmony cost and the insider-outsider theory (Lindbeck and Snower 1988) deserve mention as possible reasons for the nonlinearity of this series.

**4. ****Conclusion**

The linearity of the macroeconomic time series of Turkey was examined using the HLX linearity test. The analysis showed that the employment, industrial production, interest rate, and exports series were nonlinear. The existence of outliers in nonlinear series was tested using the methodology proposed by Chen and Liu (1993) to find out whether the source of nonlinearity was an outlier or not. The outliers were found in the nonlinear industrial production index, interest rate, and exports volume index series. The source of nonlinearity in the number of people employed and interest rates is not an outlier, and changing one observation value in interest rates does not have an impact on the nonlinearity of a series.

According to the results obtained for Turkey, the number of people employed, industrial production index, interest rate, and exports volume index series display nonlinearity characteristics for the period examined. It is important to use nonlinear methods in empirical studies to be carried out with these series to ensure reliability of the analysis.

**Anahtar Kelimeler**

Testing the Linearity of Macroeconomic Time Series of Turkey

**Kaynakça**