**2. Model structure**

The generalized autoregressive conditional heteroscedasticity (GARCH) approach includes the time dependencies between conditional variances and covariances between various markets and assets. Although multivariate GARCH (MGARCH) models fundamentally resemble univariate GARCH models, the significant difference between the two is the definitions of the equations that show how the covariances of multivariate models move over time. To elicit these changes, performing analysis within the framework of multivariate modeling allows the researcher to obtain results that are more realistic. From the financial perspective, it facilitates taking better risk management decisions.

Expansion from the univariate GARCH model to a model with n variables requires that random variables (εt) with n dimensions and a zero average are dependent on elements in the information set of the conditional variance–covariance matrix. If Ht with respect to ℱt−1 ′ (information set) can be measured, then the multivariate GARCH model is expressed as εt<sup>|</sup> <sup>ℱ</sup>t−1 ~N (0, Ht ). Because Ht is a variance matrix, positive definiteness should be satisfied. MGARCH models allow the researcher to solve multivariate financial models requiring the variances, and covariances to be dependent on the vector ARMA-type information set require modeling the variances and covariances. To explain time dependency, Bollerslev et al. [19] expanded univariate ARCH/GARCH models with multivariate models under VEC parameterization. Because the VEC-GARCH model requires the estimation of too many parameters, and the positive definiteness of the covariance matrix cannot be satisfied always, it has some inherent applicability problems. Moreover, developing MGARCH models attempt to solve the dimension problem in financial modeling. Since it is difficult to secure the positive definiteness of Ht in VEC representation without bringing serious restrictions on parameters, it is focused on alternative MGARCH model constructions. From the perspective of applicability, structures in the form of factor or diagonal parameter matrix can be incorporated into the model.

In case of uncertainty, determining the interaction of real and nominal economic variables with inflation uncertainty is important in shaping economic policies of countries experiencing problems with inflation. In this study, it is investigated whether the inflation-targeting regime causes a structural change in the economic system exposed to high- and low-inflation periods. It is aimed to contribute to the literature by focusing on the effect of inflation uncertainty on inflation, output growth and selected monetary-fiscal policy instruments under the inflation-targeting regime. Within the scope of the study, inflation-targeting period was accepted between 2003 and 2015 and preinflation-targeting period was between 1987 and 2003. The effect of inflation uncertainty on real and nominal economic indicators is examined using multivariate generalized autoregressive conditional heteroscedasticity (MGARCH) model. Because volatility is a quantitative measure of the risk that individual investors and financial institutions face, it is one of the noteworthy features of financial data. Because of the fact that financial changes move together over time, the ability to envision and forecast the dependency of second-degree moments of return is important in financial econometrics. The multivariate GARCH models, which are developed based on the fact that financial asset volatilities move together over time, provide efficiency gains. In order to handle all the possible interactions in a system equation, solutions

In this way, with the help of an equations system that is stated in a multivariate structure, all the possible interactions are tackled together and solutions are obtained based on complete information. In addition, with the help of a slope dummy variable, which was defined to differentiate the periods before and after 2003, the effects of inflation and output uncertainty have been assessed for both high and low inflation periods. The study first takes a general look at the related literature about inflation uncertainty. It then moves on to defining the model and obtaining empirical findings which were established over the model. The study concludes with an assessment section in which the empirical findings obtained are evaluated.

The generalized autoregressive conditional heteroscedasticity (GARCH) approach includes the time dependencies between conditional variances and covariances between various markets and assets. Although multivariate GARCH (MGARCH) models fundamentally resemble univariate GARCH models, the significant difference between the two is the definitions of the equations that show how the covariances of multivariate models move over time. To elicit these changes, performing analysis within the framework of multivariate modeling allows the researcher to obtain results that are more realistic. From the financial perspective, it facili-

Expansion from the univariate GARCH model to a model with n variables requires that random variables (εt) with n dimensions and a zero average are dependent on elements in the

mation set) can be measured, then the multivariate GARCH model is expressed as εt<sup>|</sup> <sup>ℱ</sup>t−1

is a variance matrix, positive definiteness should be satisfied. MGARCH

with respect to ℱt−1

′ (infor-

~N

are obtained by using full-information maximum-likelihood method.

238 Financial Management from an Emerging Market Perspective

**2. Model structure**

(0, Ht

). Because Ht

tates taking better risk management decisions.

information set of the conditional variance–covariance matrix. If Ht

This model class makes the theoretical structure of unconditional moment, ergodicity and stationarity conditions easier (He and Terasvirta, [20]). Since it is difficult to secure Ht 's positive definiteness in VEC representation without bringing serious restrictions on parameters, the Baba-Engle-Kraft-Kroner (BEKK) model, which is a restricting version of the VEC-GARCH model, is used (Engle and Kroner, [21]). As in the VEC model, the parameters of the BEKK model do not show a direct effect of the different lag terms of Ht 's elements. Structurally, the conditional covariance matrices of the BEKK-GARCH model satisfy positive definiteness. When C0 ∗ , Aik <sup>∗</sup> and Bik <sup>∗</sup> denote n x n parameter matrices, C0 ∗ denotes a triangle, C1k <sup>∗</sup> denotes J x n parameter matrices and K determines generalization of summation limit process:

$$\mathsf{H}\_{\mathsf{i}} = \mathsf{C}\_{\mathsf{0}}^{\ast^{\prime}} \mathsf{C}\_{\mathsf{0}}^{\ast} + \sum\_{\mathsf{k}=1}^{\mathsf{K}} \mathsf{C}\_{\mathsf{1k}}^{\ast^{\prime}} \mathsf{x}\_{\mathsf{t}} \mathsf{x}\_{\mathsf{t}}^{\prime} \mathsf{C}\_{\mathsf{1k}}^{\ast} + \sum\_{\mathsf{k}=1}^{\mathsf{K}} \sum\_{\mathsf{l}=1}^{\mathsf{q}} \mathsf{A}\_{\mathsf{l}\mathsf{k}}^{\ast^{\prime}} \mathsf{C}\_{\mathsf{l}\mathsf{n}+\mathsf{l}} \mathsf{A}\_{\mathsf{l}\mathsf{n}}^{\ast} + \sum\_{\mathsf{k}=1}^{\mathsf{K}} \sum\_{\mathsf{l}=1}^{\mathsf{p}} \mathsf{B}\_{\mathsf{k}}^{\ast^{\prime}} \mathsf{H}\_{\mathsf{l}\mathsf{n}} \mathsf{B}\_{\mathsf{k}}^{\ast} \tag{1}$$

can be written as BEKK (1,1,K) model. Eq. (1) is positive definite under weak conditions. In addition, because the model contains all positive-definite diagonal representations and almost all positive-definite VEC representations, it is adequately general. The BEKK model directly concentrates on the model structure, notably as A and B matrices. The main advantage of this is that because there is no constraint requirement necessitating Ht to be positive definite, parameters can be easily estimated. One disadvantage, on the other hand, is that because parameters enter the model in the form of matrices, and are transposed, effects on Ht can easily be interpreted. While matrix A measures the ARCH effect in the model, each element of the matrix B (bij) represents continuity in conditional variance from the variable "i" to the variable "j".

Using conditional variance and correlation in direct modeling of conditional covariances is a relatively new approach. Conditional correlation models are much more convenient alternatives in the estimation and interpretation of parameters. These models, which are nonlinear combinations of univariate GARCH models, allow for separate determination of individual conditional variances on the one hand, and of a conditional correlation matrix between the individual series on the other, or of another dependency criterion. Time-dependent correlations are usually calculated by the cross product of returns and by multivariate GARCH models that are linear in their squares. The dynamic conditional correlation (DCC) model takes the change of conditional correlation over time into account. The multivariate models that are called DCC have the flexibility of parsimonious parametric models and relevant univariate GARCH models for correlations. In other words, the DCC estimators have the flexibility of univarate GARCH; however, they refrain from the complexity of multivariate GARCH. Despite being nonlinear, they can be calculated by two-step methods or single-variable methods that are based on probability function. These models, which directly parameterize the conditional correlations, can be estimated in two steps: the first being a series of univariate GARCH estimations and the second being correlation estimation. It is observed that under many circumstances they function well and provide reasonable empirical results.

When εt <sup>=</sup> Dt −1 rt and Dt <sup>=</sup> diag{<sup>√</sup> \_\_\_ hi,t}, R <sup>=</sup> <sup>E</sup>t−1(εt εt ′ ) = Dt −1 Ht Dt −1 represents a correlation matrix containing conditional correlations:

$$\mathsf{H}\_{i} = \mathsf{D}\_{i}\mathsf{R}\mathsf{D}\_{i} \tag{2}$$

The dynamic conditional correlation model, which is a generalized form of the constant conditional correlation (CCC) estimator, is shown as follows:

$$\mathsf{H}\_{\mathfrak{t}} = \mathsf{D}\_{\mathfrak{t}} \mathsf{R}\_{\mathfrak{t}} \mathsf{D}\_{\mathfrak{t}} \tag{3}$$

The only difference in the dynamic conditional correlation model is that R changes over time (Engle, [22]). Parameterization of R requires that conditional variances are in integrity, and it has the same requirements as H.

The possible simplest and best method is exponential smoothing, which is expressed as a geometrical weighted average of normalized residuals. Another alternative is obtained using the GARCH (1,1) model. When the equation is written as

$$\mathfrak{q}\_{i\_0 \mathfrak{a}} = \overline{\mathfrak{p}}\_{i\_0} + \alpha (\varepsilon\_{i^{\mathfrak{a}-1}} \varepsilon\_{j \mathfrak{a}-1} - \mathfrak{q}\_{i\_0}) + \beta (\mathfrak{q}\_{i\_0 j \mathfrak{a}-1} - \overline{\mathfrak{p}}\_{i\_0}) \tag{4}$$

the below equation

$$\mathbf{q}\_{\downarrow\_{\downarrow}\downarrow} = \overline{\rho}\_{\downarrow\downarrow} \left( \frac{1-\alpha-\beta}{1-\beta} \right) + \alpha \sum\_{s=1,\ast} \beta^s \,\varepsilon\_{\downarrow\downarrow-s} \,\varepsilon\_{\downarrow\uparrow\star s} \tag{5}$$

is obtained. Assuming that the unconditional expectation of the cross product is <sup>ρ</sup> ¯, variances are <sup>ρ</sup> ¯i,j <sup>=</sup> 1. Because the <sup>t</sup> <sup>=</sup> <sup>|</sup>qi,j,t | covariance matrix is positive definite and the weighted average of the positive semi-definite matrix, the correlation estimator ρi,j,t <sup>=</sup> <sup>q</sup> \_\_\_\_\_\_ i,j,t √ \_\_\_\_\_\_\_ qi,i,t qj,j,t is positive definite.

When S is an unconditional correlation matrix of epsilons, the matrix forms of these estimators are written as

$$\mathcal{Q}\_{\mathfrak{t}} = (1 - \lambda) (\varepsilon\_{\mathfrak{t}-\mathfrak{t}} \varepsilon\_{\mathfrak{t}-\mathfrak{t}}') + \lambda \, \mathcal{Q}\_{\mathfrak{t}-\mathfrak{t}} \tag{6}$$

$$\mathcal{Q}\_{\mathfrak{e}} = \mathsf{S}(\mathsf{I} - \mathsf{a} - \beta) + \alpha (\varepsilon\_{\mathfrak{e} \mapsto 1} \varepsilon\_{\mathfrak{e} \mapsto 1}') + \beta \, \mathcal{Q}\_{\mathfrak{e} \mapsto 1} \tag{7}$$

As long as unconditional moments are adapted to a simple correlation matrix, in order to parameterize the correlations, more complex positive-definite multivariate GARCH models can be used.

#### **3. Effects of inflation uncertainty on economic policies**

that are called DCC have the flexibility of parsimonious parametric models and relevant univariate GARCH models for correlations. In other words, the DCC estimators have the flexibility of univarate GARCH; however, they refrain from the complexity of multivariate GARCH. Despite being nonlinear, they can be calculated by two-step methods or single-variable methods that are based on probability function. These models, which directly parameterize the conditional correlations, can be estimated in two steps: the first being a series of univariate GARCH estimations and the second being correlation estimation. It is observed that under many circumstances they function well and provide reasonable empirical results.

When εt <sup>=</sup> Dt

−1 rt

taining conditional correlations:

has the same requirements as H.

,, = ρ¯,

,, = ρ¯,(

¯i,j <sup>=</sup> 1. Because the <sup>t</sup> <sup>=</sup> <sup>|</sup>qi,j,t

the below equation

are <sup>ρ</sup>

definite.

tors are written as

and Dt <sup>=</sup> diag{<sup>√</sup>

240 Financial Management from an Emerging Market Perspective

\_\_\_

ditional correlation (CCC) estimator, is shown as follows:

GARCH (1,1) model. When the equation is written as

<sup>=</sup> (1 <sup>−</sup> λ)(ε−1 <sup>ε</sup>−1

= ( − α − β) + α(ε−1 ε−1

hi,t}, R <sup>=</sup> <sup>E</sup>t−1(εt

εt ′ ) = Dt −1 Ht Dt −1

= (2)

The dynamic conditional correlation model, which is a generalized form of the constant con-

= (3)

The only difference in the dynamic conditional correlation model is that R changes over time (Engle, [22]). Parameterization of R requires that conditional variances are in integrity, and it

The possible simplest and best method is exponential smoothing, which is expressed as a geometrical weighted average of normalized residuals. Another alternative is obtained using the

<sup>1</sup> <sup>−</sup> <sup>α</sup> <sup>−</sup> <sup>β</sup> \_\_\_\_\_

is obtained. Assuming that the unconditional expectation of the cross product is <sup>ρ</sup>

age of the positive semi-definite matrix, the correlation estimator ρi,j,t <sup>=</sup>

<sup>1</sup> <sup>−</sup> <sup>β</sup> ) + α ∑

When S is an unconditional correlation matrix of epsilons, the matrix forms of these estima-

=1,∞

<sup>+</sup> α(ε,−1 <sup>ε</sup>,−1 <sup>−</sup> <sup>ρ</sup>¯,) <sup>+</sup> β(,,−1 <sup>−</sup> <sup>ρ</sup>¯,) (4)


β ε,− ε,− (5)

′ ) + λ −1 (6)

′ ) + β −1 (7)

<sup>q</sup> \_\_\_\_\_\_ i,j,t √ \_\_\_\_\_\_\_ qi,i,t qj,j,t

¯, variances

is positive

represents a correlation matrix con-

Quarterly data (1987:Q1–2015: Q3) were used to examine the effect of inflation uncertainty for Turkey on the variables of consumer price index, real gross domestic product, real effective exchange rate, 12-month deposit interest rate, government expenditures and tax revenues. The data set was taken from the Central Bank of the Republic of Turkey (CBRT) electronic data distribution system (EVDS). Different term dates for different base years are organized according to the 1987 base year. The seasonal structure in the real gross national product, government expenditures and tax revenue variables is eliminated by using the Tramo/Seat method. The government expenditures and tax revenues series are divided by the seasonally adjusted nominal gross national product and multiplied by 100. Growth measures expressed as percentage changes are obtained by taking the logarithmic first-order differences, multiplying by 100, of the consumer price index, real gross domestic product, 12-month deposit interest rate and real effective exchange rate.

MGARCH model structure by using inflation (πt ), output growth (bt ),exchange rate change (dt ), interest rate change (f t ), governmentexpenditures (kht ), tax revenues (vgt ), dummy variable (*Dk* ) and inflation uncertainty (hπt )

$$\boldsymbol{\pi}\boldsymbol{\pi}\_{\boldsymbol{i}} = \mathbf{a}\_{0} + \mathbf{a}\_{1}\boldsymbol{\mathsf{D}}\_{k} + \sum\_{i=1}^{p} \mathbf{a}\_{2i}\boldsymbol{\pi}\_{\boldsymbol{i}+i} + \sum\_{\boldsymbol{r}\boldsymbol{l}}^{p} \mathbf{a}\_{3i}\mathbf{b}\_{\boldsymbol{r}+i} + \sum\_{\boldsymbol{r}\boldsymbol{l}}^{p} \mathbf{a}\_{4i}\mathbf{d}\_{\boldsymbol{r}+i} + \sum\_{\boldsymbol{r}\boldsymbol{l}}^{p} \mathbf{a}\_{5i}\mathbf{k}\mathbf{h}\_{\boldsymbol{r}+i} + \sum\_{\boldsymbol{r}\boldsymbol{l}}^{p} \mathbf{a}\_{7i}\mathbf{v}\mathbf{g}\_{\boldsymbol{r}+i} + \boldsymbol{\eth}\_{1}\sqrt{\boldsymbol{h}\_{\pi\_{\boldsymbol{i}}}} + \boldsymbol{\gamma}\_{1}\boldsymbol{\mathsf{D}}\_{k}\sqrt{\boldsymbol{h}\_{\pi\_{\boldsymbol{i}}}} + \boldsymbol{\varepsilon}\_{\text{in}} \tag{8}$$

$$\mathbf{b}\_{i} = \mathbf{b}\_{0} + \mathbf{b}\_{1}\ \mathbf{D}\_{k} + \sum\_{i=1}^{p} \mathbf{b}\_{2i}\ \pi\_{i+} + \sum\_{i=1}^{p} \mathbf{b}\_{3i}\ \mathbf{b}\_{i+} + \sum\_{i=1}^{p} \mathbf{b}\_{4i}\ d\_{i+} + \sum\_{i=1}^{p} \mathbf{b}\_{5i}\ \mathbf{f}\_{i+} + \sum\_{i=1}^{p} \mathbf{b}\_{6i}k\mathbf{h}\_{i+} + \sum\_{i=1}^{p} \mathbf{b}\_{7i}\ \mathbf{v}\mathbf{g}\_{i+} + \boldsymbol{\eth}\_{2}\sqrt{\boldsymbol{h}\_{\pi\_{i}}} + \boldsymbol{\gamma}\_{2}\boldsymbol{\mathcal{D}}\_{k}\sqrt{\boldsymbol{h}\_{\pi\_{i}}} + \boldsymbol{\varepsilon}\_{2} \quad \text{(9)}$$

$$\mathbf{d}\_{i} = \mathbf{d}\_{0} + \mathbf{d}\_{1}\mathbf{D}\_{k} + \sum\_{i=1}^{p} \mathbf{d}\_{ii}\pi\_{i+i} + \sum\_{i=1}^{p} \mathbf{d}\_{3i}\mathbf{b}\_{i+i} + \sum\_{i=1}^{p} \mathbf{d}\_{4i}\mathbf{d}\_{i+i} + \sum\_{i=1}^{p} \mathbf{d}\_{5i}\mathbf{f}\_{i+i} + \sum\_{i=1}^{p} \mathbf{d}\_{7i}k\mathbf{b}\_{i+i} + \sum\_{i=1}^{p} \mathbf{d}\_{7i}\mathbf{v}\mathbf{g}\_{i+i} + \mathbf{b}\_{3}\sqrt{\overline{h}\_{\pi\_{i}}} + \gamma\_{3}\mathbf{D}\_{k}\sqrt{\overline{h}\_{\pi\_{i}}} + \boldsymbol{\varepsilon}\_{\chi\_{i}} \tag{10}$$

$$\mathbf{f}\_{i} = \mathbf{f}\_{0} + \mathbf{f}\_{i}\mathbf{D}\_{k} + \sum\_{i=1}^{p} \mathbf{f}\_{zi}\mathbf{r}\_{i:i} + \sum\_{i=1}^{p} \mathbf{f}\_{qi}\mathbf{b}\_{:i} + \sum\_{i=1}^{p} \mathbf{f}\_{qi}\mathbf{d}\_{:i} + \sum\_{i=1}^{p} \mathbf{f}\_{qi}\mathbf{f}\_{ri} + \sum\_{i=1}^{p} \mathbf{f}\_{qi}k\mathbf{h}\_{:i} + \sum\_{i=1}^{p} \mathbf{f}\_{qi}\mathbf{v}\mathbf{g}\_{ri} + \boldsymbol{\eth}\_{\mathbf{d}} \left| \overline{\boldsymbol{h}\_{\pi\_{i}}} + \boldsymbol{\gamma}\_{\mathsf{d}} \boldsymbol{D}\_{\boldsymbol{\mathsf{k}}} \right| \overline{\boldsymbol{h}\_{\pi\_{i}}} + \boldsymbol{\varepsilon}\_{\mathsf{a}} \tag{11}$$

$$\mathbf{k}\mathbf{h}\_{\boldsymbol{\iota}} = \mathbf{k}\_{0} + \mathbf{k}\_{1}\mathbf{D}\_{\boldsymbol{\iota}} + \sum\_{i=1}^{p} \mathbf{k}\_{\boldsymbol{\omega}}\boldsymbol{\pi}\_{\boldsymbol{\iota}+i} + \sum\_{i=1}^{p} \mathbf{k}\_{\boldsymbol{\omega}}\mathbf{b}\_{\boldsymbol{\iota}+i} + \sum\_{i=1}^{p} \mathbf{k}\_{\boldsymbol{\omega}}\mathbf{d}\_{\boldsymbol{\iota}+i} + \sum\_{i=1}^{p} \mathbf{k}\_{\boldsymbol{\alpha}}\mathbf{k}\boldsymbol{\theta}\_{\boldsymbol{\iota}+i} + \sum\_{i=1}^{p} \mathbf{k}\_{\boldsymbol{\alpha}}\mathbf{v}\mathbf{g}\_{\boldsymbol{\iota}+i} + \boldsymbol{\Theta}\_{\boldsymbol{\Xi}} \left| \overline{\boldsymbol{h}\_{\boldsymbol{\omega}}} + \boldsymbol{\gamma}\_{\boldsymbol{\Xi}}\mathbf{D}\_{\boldsymbol{\iota}} \sqrt{\overline{\boldsymbol{h}\_{\boldsymbol{\omega}}}} + \boldsymbol{\varepsilon}\_{\boldsymbol{\Xi}}\mathbf{1} \right| \mathbf{1} \mathbf{2} \mathbf{3}$$

$$\mathbf{v\_{i}}\mathbf{g\_{i}} = \mathbf{v\_{0}} + \mathbf{v\_{i}}\mathcal{D}\_{\mathbf{s}} + \sum\_{i=1}^{p} \mathbf{v\_{i}}\pi\_{\mathbf{s}i} + \sum\_{i=1}^{p} \mathbf{v\_{i}}\mathbf{b\_{i}}\_{\mathbf{s}i} + \sum\_{i=1}^{p} \mathbf{v\_{a}}\mathcal{d}\_{\mathbf{s}i} + \sum\_{i=1}^{p} \mathbf{v\_{i}}\mathbf{f\_{i}}\_{\mathbf{s}i} + \sum\_{i=1}^{p} \mathbf{v\_{a}}k\hbar\_{\mathbf{s}i} + \sum\_{i=1}^{p} \mathbf{v\_{j}}\mathbf{v\_{i}}\mathbf{g\_{i}}\_{\mathbf{s}i} + \boldsymbol{\delta}\_{\boldsymbol{\delta}} \left| \overline{\boldsymbol{h}\_{\pi\_{\mathbf{s}}}} + \boldsymbol{\gamma}\_{\boldsymbol{\delta}} \boldsymbol{\mathcal{D}}\_{\boldsymbol{k}} \right| \overline{\boldsymbol{h}\_{\pi\_{\mathbf{s}}}} + \boldsymbol{\varepsilon}\_{\boldsymbol{\alpha}} \tag{13}$$

$$\boldsymbol{\varepsilon}\_{\rm tr} = \sqrt{\boldsymbol{h}\_{\pi\_{\rm v}}}^{\*} \mathbf{z}\_{\rm v} \tag{14}$$

is performed. The mean-model structure consists of Eqs. (8)–(13). Agumented Dickey-Fuller (ADF), Kwiatkowski-Phillips-Schmidt-Shin (KPSS) and Phillips-Perron (PP) unit root tests were applied in **Table 1** to set out the stationarity of the variables. It is decided that all variables are stationary, generally, when the ADF, KPSS and PP stationarity test results are evaluated for all variables.

**Figure 1** shows the tendencies of the series used in the model construction with respect to time. When the inflation series is examined, it is observed that there has been a fluctuation in the period of 2003 with the transition to the inflation-targeting regime. A dummy variable has been added to the model structure to reveal the effects of this period. Dummy variable(*Dk* ) used in the model construction is defined as 1 for the quarter of 2003–2015 and 0 for the other periods.

In the one-dimensional case, the mean equation for the model should be decided. In addition, the first condition that must be satisfied before dealing with the general structure of the variance equation in the multivariate GARCH model is that the series should be a white noise vector process. Residuals should be serially uncorrelated to each other, as well as have zero correlation with the lags of other components. It is suggested to use low-order VAR models to get rid of nested autocorrelation structure. **Table 2** shows the optimal lag length calculated for the model structure.

Detection of autocorrelation in residuals and/or squared residuals within the framework of established VAR (1) model leads to the use of MGARCH models. A preliminary multivariate ARCH effect test was performed in order to question the existence of the ARCH effect on the model constructed. In **Table 3**, it is shown that the absence of the ARCH effect is strictly rejected. Since the null hypothesis, constant and all other lagged parameters are equal to zero and are rejected, it can be said that there is no constant correlation and a dynamic structure can be mentioned with strong time-dependency correlation between the selected variables.

1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 2011 2013 2015

**Figure 1.** Graphical representation of the tendency of the series used in model construction over time.

Effects of Inflation Uncertainty on Economic Policies: Inflation-Targeting Regime http://dx.doi.org/10.5772/intechopen.71625 243


\*\*\*0.01, \*\*0.05 and \*0.10 test critical values.

**Table 1.** Unit root test results.

is performed. The mean-model structure consists of Eqs. (8)–(13). Agumented Dickey-Fuller (ADF), Kwiatkowski-Phillips-Schmidt-Shin (KPSS) and Phillips-Perron (PP) unit root tests were applied in **Table 1** to set out the stationarity of the variables. It is decided that all variables are stationary, generally, when the ADF, KPSS and PP stationarity test results are evalu-

**Figure 1** shows the tendencies of the series used in the model construction with respect to time. When the inflation series is examined, it is observed that there has been a fluctuation in the period of 2003 with the transition to the inflation-targeting regime. A dummy variable has been

the model construction is defined as 1 for the quarter of 2003–2015 and 0 for the other periods. In the one-dimensional case, the mean equation for the model should be decided. In addition, the first condition that must be satisfied before dealing with the general structure of the variance equation in the multivariate GARCH model is that the series should be a white noise vector process. Residuals should be serially uncorrelated to each other, as well as have zero correlation with the lags of other components. It is suggested to use low-order VAR models to get rid of nested autocorrelation structure. **Table 2** shows the optimal lag length calculated for the model structure. Detection of autocorrelation in residuals and/or squared residuals within the framework of established VAR (1) model leads to the use of MGARCH models. A preliminary multivariate ARCH effect test was performed in order to question the existence of the ARCH effect on the model constructed. In **Table 3**, it is shown that the absence of the ARCH effect is strictly rejected. Since the null hypothesis, constant and all other lagged parameters are equal to zero and are rejected, it can be said that there is no constant correlation and a dynamic structure can be mentioned with strong time-dependency correlation between the selected variables.

> -80 -60 -40 -20 0 20 40 60

ft

3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 vgt

kht

**Figure 1.** Graphical representation of the tendency of the series used in model construction over time.

) used in

1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 2011 2013 2015

1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 2011 2013 2015

1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 2011 2013 2015

added to the model structure to reveal the effects of this period. Dummy variable(*Dk*

ated for all variables.

242 Financial Management from an Emerging Market Perspective

1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 2011 2013 2015

1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 2011 2013 2015

1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 2011 2013 2015

bt

dt

πt




\*minimum value on each information criteria for model order selection.

**Table 2.** Lag-length selection for model structure.


**Table 3.** The presence of a priori ARCH effect.



**Panel A: Model parameter tahminleri**

**π***<sup>t</sup>* Constant

*πt*−1 bt−1 d*t*−1

f

0.033\*\*

f

−0.028\*

f

0.083\*

f

0.190\*

f

0.874\*

f

−0.323\*

*t*−1

*t*−1

*t*−1

*t*−1

*t*−1

*t*−1

kh*t*−1 Vg*t*−1

*D<sup>k</sup>*

h<sup>t</sup> *D<sup>k</sup>*

h<sup>t</sup>

−0.12\*

Panel B: GARCH parameter estimates

C(1) C(2) C(3)

5.267\*\*

C(6)

9.157\*\*\*

A(3)

0.709\*\*\*

A(6)

0.222\*\*\*

B(3)

0.235\*

B(6)

0.534

2.009\*

C(5)

8.372\*\*\*

A(2)

0.365

A(5)

0.352\*\*\*

B(2)

0.514\*\*\*

B(5)

0.583\*\*\*

3.019\*\*\*

C(4)

4.620\*\*\*

A(1)

0.546\*

A(4)

0.409\*\*

B(1)

0.245\*\*\*

B(4)

0.480\*\*\*

*D<sup>k</sup>*

h<sup>t</sup>

−0.362\*

*D<sup>k</sup>*

h<sup>t</sup>

0.023

*D<sup>k</sup>*

h<sup>t</sup>

0.102\*

*D<sup>k</sup>*

h<sup>t</sup>

−0.878\*

*D<sup>k</sup>*

h<sup>t</sup>

0.247\*

∗

∗

∗

∗

∗

∗

0.479\*

h<sup>t</sup>

0.155\*\*

h<sup>t</sup>

0.045

h<sup>t</sup>

−0.093\*

h<sup>t</sup>

0.679\*\*

h<sup>t</sup>

−0.18\*

−0.48\*

*D<sup>k</sup>*

−0.095\*

*D<sup>k</sup>*

0.995

*D<sup>k</sup>*

0.689\*

*D<sup>k</sup>*

−1.000\*

*D<sup>k</sup>*

0.154\*

0.074

Vg*t*−1

0.013

Vg*t*−1

0.053\*

Vg*t*−1

0.042

Vg*t*−1

0.092\*

Vg*t*−1

0.463\*

0.001

kh*t*−1

−0.021

kh*t*−1

0.314

kh*t*−1

0.093\*

kh*t*−1

0.021

kh*t*−1

0.084

−0.567

d*t*−1

0.043\*

d*t*−1

0.092

d*t*−1

−0.308\*\*

d*t*−1

0.092\*

d*t*−1

0.443\*

0.126

bt−1

−0.042

bt−1

0.114

bt−1

0.526\*

bt−1

0.522

bt−1

0.982\*\*

244 Financial Management from an Emerging Market Perspective

0.630\*

*πt*−1

−0.026

*πt*−1

0.120

*πt*−1

0.105\*

*πt*−1

−0.101

*πt*−1

0.242

4.10**\***

Constant

0.65\*

Constant

−0.750

Constant

−1.013\*

Constant

2.001\*

Constant

−1.327\*

**b***<sup>t</sup>*

**d***<sup>t</sup>*

**f**

**kh***t*

**vg***t*

*t*

**Table 4.** DCC model parameter estimation results. Within the scope of the study, the model structure is examined as a dynamic conditional correlation model to determine the effect of inflation uncertainty on economic variables. For this reason, the volatilities of the involved variables are restricted within the DCC framework. The DCC model established in the study states that there are unstable interactions of the series concerned with conditional correlation and that this correlation affects the correlations with a one lag-period. The DCC model estimation results are shown in **Table 4**. According to the result of the multivariate Q statistic in **Table 4**, no residuals were found to be serially correlated, and the ARCH effect was no more observed in the model. It is found that there is no autocorrelation problem when considering the autocorrelation function of residuals and its squares. When these results are taken into consideration, the effect of uncertainty in the inflation can be evaluated using the DCC model. The DCC model provides more precisely the dynamic structure of the correlation between inflation uncertainty and macroeconomic variables.

The dummy variable used for inflation targeting was found to be statistically insignificant for exchange rate changes, while statistically significant for inflation, output growth, interest rate change, governmet expenditure and tax revenues. This result indicates the effect of inflation uncertainty on selected variables differs pre-2003 and post-2003 periods. In other words, the effects of inflation uncertainty on real and nominal economic indicators are not the same in high and low inflationary periods. Inflation uncertainty had a positive and statistically significant effect on inflation, a positive and statistically significant effect on output gowth, a positive and statistically insignificant effect on exchange rate change, a negative and statistically significant effect on interest rate change, a positive and statistically significant effect on government expenditures and negative and statistically significant effect on tax revenues pre-2003 period. In the post-2003, inflation uncertainty affects inflation positively and statistically, output growth negatively and statistically significant, exchange rate change positively and statistically insignificant, interest rate change positively and statistically significant, government expenditures negatively and statistically significant, and tax revenues positively and statistically significant.
