- Email: [email protected]

S1544-6123(14)00058-0 http://dx.doi.org/10.1016/j.frl.2014.10.002 FRL 322

To appear in:

Finance Research Letters

Received Date: Accepted Date:

23 July 2014 3 October 2014

Please cite this article as: Zhu, X., Zhu, Y., European business cycles and stock return predictability, Finance Research Letters (2014), doi: http://dx.doi.org/10.1016/j.frl.2014.10.002

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European business cycles and stock return predictability∗ Xiaoneng Zhu† Central University of Finance and Economics Yanjian Zhu‡ Zhejiang University This Draft: July 15, 2014 JEL Classifications: G1, E4, F3. Keywords: Stock returns, economic value, European business cycles, return predictability.

∗ We thank the Editor, an anonymous referee, Jie Zhu, Zhongda He, and Feng Guo. Xiaoneng Zhu acknowledges the financial support from the Natural Science Foundation of China (Grant No. 71473281). † Email: [email protected] ‡ Corresponding author: The Academy of Financial Research, College of Economics, Zhejiang University, Zheda Road #38, Hangzhou, China. Phone: 86-571-89938072; Fax:86-571-89938075; Email: [email protected]

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European business cycles and stock return predictability

This draft: July 15, 2014 JEL Classifications: G1, E4, F3. Keywords: Stock returns, economic value, European business cycles, return predictability.

Abstract This paper finds that the European leading economic indicator, a prime business cycle indicator for the European economies published by the OECD, can strongly predict European stock returns and generate utility gains. Importantly, the predictive power of the European indicator is above and beyond that contained in the country-specific leading indicator. Furthermore, we find that the predictive power of the European indicator is stable.

1

Introduction

Conventional wisdom views the market’s expectation of future economic conditions as an important driver of stock price movements. The classic Merton (1973) model provides the theoretical basis for this view: as economic fluctuations affect future consumption and investment opportunities, indicators related to future economic conditions are key state variables in intertemporal asset pricing models. Empirically, a large literature has investigated the predictability of stock returns using macroeconomic indicators. In particular, some prime business cycle indicators have been identified as the predictor of stock returns such as aggregate output (e.g., Balvers, Cosimano, and McDonald, 1990), the output gap (e.g., Cooper and Priestley, 2008), production growth rates (e.g., Fama, 1990; Schwert, 1990), and the leading economic indicator (e.g., Huang and Zhou, 2013). This paper uncovers a powerful common predictor of European stock returns: a European leading economic indicator (ELEI), which is a measure of the overall state of the European economies published by the OECD. The economic foundation for the use of ELEI is the recent works of Kose, Otrok, and Whiteman (2003), Artis (1997), and Artis, Krolzig, and Toro (2004), who demonstrate the presence of a significant European business cycle. Given intimate links across the European economies, ELEI may contain important information about economic conditions in the European countries, above and beyond that contained in the country-specific leading economic indicator (CLEI). Hence, ELEI may predict European stock returns better than CLEI in the European stock market. We contribute to the literature in two aspects. First, we investigate the predictive power of ELEI and compare the predictive ability of ELEI with that of CLEI. This type of analysis provides insights on the integration of European stock markets. It also sharpens our understanding on the nature of stock return predictability. Second, we investigate the predictability of European stock returns using CLEI. Despite the evidence regarding the predictive ability of aggregate economic indicators in the US stock 1

market, there have been surprisingly few attempts to examine the predictive power of prime business cycle indicators in other markets. Our analysis using international data sheds new light on the predictive ability of prime business cycle indicators. To preview our results, we find that CLEI outperforms the historical average. Indeed, the out-of-sample R-square (e.g., Campbell and Thompson, 2008) ranges between 1.3% and 8.5% and is statistically significant. What is more striking is that ELEI generally outperforms CLEI in terms of out-of-sample forecasting performance. The encompassing test suggests that the better forecasting performance of ELEI is usually significant. Furthermore, the Fluctuation test indicates that the out-performance of ELEI is relatively stable over the entire out-of-sample period. Since statistical significance does not necessarily imply economic significance, we also assess the economic value of ELEI and CLEI in asset allocation. We find that ELEI generally delivers significant economic gains. In contrast, the economic value of CLEI is usually negative. Overall, ELEI is a statistically and economically meaningful common predictor of European stock returns. We also conduct the in-sample analysis. The in-sample evidence further confirms that the ELEI forecasting model outperform the CLEI forecasting model. To test the robustness of the in-sample evidence, we run augmented regressions with both ELEI and CLEI as regressors. The augmented regression shows that ELEI is usually significant. In contrast, CLEI often becomes insignificant. These results indicate that ELEI is a stronger predictor of international stock returns than CLEI is. Broadly speaking, our findings are consistent with those earlier studies that have looked at return predictability. For instance, Harvey (1991), Ilmanen (1995), and Zhou and Zhu (2014) find that global instruments are better predictors than local instruments in international financial markets. The paper proceeds as follows: Section 2 presents the econometric methodology and the measure for evaluating economic gain. Section 3 presents the out-of-sample forecasting results. Section 4 conducts the in-sample analysis. Section 5 concludes.

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2

Methodology

A standard forecasting specification regresses an independent lagged predictor on stock returns

rt+1 = α + βxt + εt+1 ,

(1)

where rt+1 is the stock return, and xt is a variable whose predictive ability is of interest. Following Campbell and Thompson (2008) and Welch and Goyal (2008), the historical P average of stock returns, r¯t+1 = T1 Tt=1 rt , serves as a natural benchmark forecasting model. Intuitively, if xt contains information for predicting stock returns, then rˆt+1 , the forecast based on xt , should perform better than r¯t+1 . 2 To measure the forecasting performance, we use the out-of-sample R2 statistic, ROS ,

suggested by Campbell and Thompson (2008) to compare the rˆt+1 and r¯t+1 forecasts. 2 Specifically, the ROS is given by

XT −1 2 ROS

=1−

t=0 XT −1 t=0

(rt+1 − rˆt+1 )2 .

(2)

(rt+1 − r¯t+1 )2

2 The ROS statistic measures the reduction in mean square prediction error (MSPE). 2 When ROS > 0, the rˆt+1 forecast outperforms the r¯t+1 forecast according to the MSPE

metric. 2 The ROS statistic is a point estimate of forecast accuracy. To test whether two

competing models have statistically differences in forecasting accuracy, Clark and West 2 (2007) develop an MSPE-adjusted statistic to test the null hypothesis of ROS ≥ 0 2 against the alternative of ROS < 0. The Clark-West statistic is conveniently computed

by first defining ft+1 = (rt+1 − r¯t+1 )2 − [(rt+1 − rˆt+1 )2 − (¯ rt+1 − rˆt+1 )2 ].

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(3)

By regressing ft+1 on a constant and computing the t-statistic corresponding to the constant, a p-value for a one-sided (upper tail) test is obtained with the standard normal distribution. To compare the information content in ELEI and CLEI forecasts, we use the forecast encompassing test. Consider two forecasting models i and j providing two forecasts rˆi,t+1 and rˆj,t+1 , the optimal forecast is given by ∗ rˆt+1 = (1 − λ)ˆ ri,t+1 + λˆ rj,t+1 ,

(4)

where 0 ≤ λ ≤ 1. The intuition of forecast encompassing is straightforward: λ = 0 implies that the model i forecast encompasses the model j forecast, as model j does not contain additional useful information beyond that contained in model i for predicting stock returns. In contrast, λ > 0 indicates that the model i forecast does not encompass the model j forecast since the model j forecast is useful for forming the optimal forecast. Harvey, Leybourne, and Newbold (1998, HLN henceforth) develop a statistic to test the null hypothesis that the model i forecast encompasses the model j forecast against the (one-sided) alternative hypothesis that the model i forecast does not encompass the model j forecast. Define dt+1 = (ˆ ui,t+1 − uˆj,t+1 )ˆ ui,t+1 , where uˆi,t+1 = rt+1 − rˆi,t+1 XT and uˆj,t+1 = rt+1 − rˆj,t+1 . Letting d¯ = T1 dt , the modified version of the HLN t=1

statistic can be expressed as ¯ −1/2 ]d, ¯ ˆ d) M HLN = T 1/2 [Q(

(5)

¯ = 1 Vˆ (d) ¯ with Vˆ (d) ¯ being the sample variance of {dt }T . HLN recommend ˆ d) where Q( t=1 T using the MHLN statistic and the tT distribution to assess statistical significance. 2 The ROS is a measure of statistical significance. However, statistical significance 2 does not necessarily imply economic significance. In particular, the ROS measure does

not explicitly account for the risk borne by an investor over the out-of-sample period. To assess the economic value of a forecasting model, we follow Campbell and Thompson

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(2008) and Welch and Goyal (2008) to compute realized utility gains accrued to a mean-variance investor on a real-time basis. Assume that the investor with relative risk aversion parameter γ allocates her portfolio monthly between stocks and risk-free bills using forecasts of the historical average. At the end of period t, the investor will decide to allocate the following share of her portfolio to equities in period t + 1: w0,t =

1 r¯t+1 , γσ ˆ 2t+1

(6)

where σ ˆ 2t+1 is the rolling-window estimate of the variance of stock returns. Over the out-of-sample period, the investor realizes an average utility level of 1 2 v0 = µ ¯ − γσ ¯ , 2

(7)

where µ ¯ and σ ¯ 2 are respectively the sample mean and variance over the out-of-sample period for the return on the benchmark portfolio formed using stock return forecasts based on the historical average. When the investor predicts stock returns using leading economic indicators, she will choose an equity share of w1,t =

1 rˆt+1 . γσ ˆ 2t+1

(8)

Over the out-of-sample period, the investor realizes an average utility level of 1 2 v1 = µ ˆ − γσ ˆ , 2

(9)

where µ ˆ and σ ˆ 2 are respectively the sample mean and variance over the out-of-sample period for the return on the benchmark portfolio formed using excess return forecasts based on leading economic indicators. In our empirical analysis, the economic gain of leading economic indicators is the difference between equation (9) and equation (7), ∆ = 1200(v1 − v0 ).

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(10)

We multiply the difference by 1200 to express in average annualized percentage return.

3

Out-of-sample results

We predict stock returns for twelve European countries: Austria, Belgium, Denmark, France, Germany, Italy, the Netherlands, Norway, Spain, Sweden, Swiss, and the United Kingdom.1 The monthly country index returns for these markets are from Thomson Financial’s Datastream series in local currencies. We form excess stock returns by subtracting the appropriately de-annualized short-term interest rate from country index returns. The sample period is 1980:01-2013:07 Table 1 reports the summary statistics for monthly stock returns (in percent) for the European countries. Two predictors we consider in this paper are CLEI and ELEI, which are complied by the OECD.2 LEI is designed to provide early signals of turning points in business cycles. In our out-of-sample forecasting exercise, instead of directly using LEI to predict stock returns, we use the month-over-month log changes in LEI to forecast stock returns. By using log changes, we remove the trend from LEI. More importantly, relative changes in economic conditions can better capture investors’ relative risk aversion, as emphasized by Ilmanen (1995).

[Insert Table 1, Table 2 about Here]

As in Welch and Goyal (2008), we generate out-of-sample forecasts of stock returns using a recursive (expanding) estimation window. Specifically, we estimate and forecast recursively, using data from 1980:01 to the time that the forecast is made, beginning in 1990:01 and extending through 2013:07. We emphasize that this out-of-sample forecasting exercise simulates the situation of a forecaster in real time. 1

The standard point of data availability determines the sample markets. We use vintage data for out-of-sample forecasting. To avoid look-forward bias, we recursively adjust seasonality in LEI. 2

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2 Column (1) of Table 2 reports ROS statistics for the CLEI predictive model relative 2 to the historical average. We find that CLEI consistently deliver positive ROS statistic,

suggesting that CLEI contains information about future stock returns. The Clark2 West (2007) M SP E-adjusted statistics further reveal that these positive ROS s are

statistically significant. Column (2) presents the utility gains from an asset allocation perspective by setting γ = 3.3 We find that the economic value of CLEI is typically negative or small, suggesting that investors cannot economically benefit from using the information contained in CLEI. Columns (3) and (4) of Table 2 report the results for the ELEI predictive model relative to the historical average. We find that ELEI consistently delivers significant 2 positive ROS statistics, which are generally higher than those generated by CLEI. Fur-

thermore, ELEI delivers systematic economic gain. Our results seem to indicate that ELEI is a better predictor of stock returns than CLEI is. To formally test the better forecasting performance of the ELEI model, we conduct the encompassing test. Column (5) of Table 2 reports p-values for the M HLN statistic applied to the 1990:01-2013:07 out-of-sample forecasts. Each entry in the column corresponds to the null hypothesis that the ELEI model encompasses the CLEI model. The null hypothesis cannot be rejected at conventional significance levels in eight markets (Austria, Belgium, France, Germany, Italy, Spain, Sweden, and UK), suggesting that the better forecasting performance of ELEI is generally significant. To further check the stability of the out-of-sample forecasting performance of the ELEI model compared to the CLEI model, we implement the two-sided Fluctuation test (see, Giacomini and Rossi, 2010). Specifically, we compare two models’ performance in rolling windows over the out-of-sample period. Measuring the performance over rolling windows allows us to compare their relative performance as the sample evolves over time. When the test statistic is above zero, the ELEI performs better than the CLEI approach. When the test statistic is above the upper critical value line, we conclude that the ELEI approach performs significantly better. 3

The results are similar for other reasonable value of γ.

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[Insert Figure 1 about Here]

In conducting the Fluctuation test, we use a rolling of window of 10 years. Figure 4 reports the test statistic together with two-sided critical values at the 5% as well as the 10% significance levels. We find that the test statistics are generally positive in all twelve markets, pointing towards a consistent better forecasting performance of the ELEI model. At the same time, we note that the Fluctuation-test statistics are often significant. Overall, our results seem to indicate that ELEI is a common predictor of European stock returns.

4

In-sample evidence

In this section, we conduct the in-sample analysis. The prediction regression is equation (1). Columns (1) and (2) of Table 3 report the results when CLEI is the regressor. The results suggest that CLEI significantly predicts stock returns in-sample in the European countries, with in-sample R2 spanning between 0.02 and 0.09. Columns (3) and (4) of Table 3 present the results for ELEI. We find that ELEI is consistently significant for predicting stock returns in all European markets. In nine out of twelve markets, ELEI delivers higher in-sample R2 than CLEI does. Columns (1) and (3) indicate that regression coefficients are consistently negative. This is consistent with previous research (e.g., Keim and Stambaugh, 1986; Fama and French, 1989), which suggests that expected returns are lower when business conditions are strong and higher when conditions are weak.

[Insert Table 3 about Here]

To further test whether ELEI contains information about future stock returns above and beyond that contained in CLEI, We run the predictive regression by including both

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ELEI and CLEI as predictors. The augmented prediction regression takes the form rt+1 = α + β 1 rt + β CLEI CLEIt + β ELEI ELEIt + εt+1 .

(11)

Columns (5) and (6) reports OLS estimates of β CLEI and β ELEI . Of the 12 β CLEI estimates in Table 3, 11 are negative; only 4 of these are significant at conventional levels. Regarding to the magnitude of β CLEI estimate, the absolute value of all estimates are less than or equal to 0.07. ELEI clearly displays stronger predictive power. Ten of the β ELEI estimates are significant, and the absolute value of these β ELEI estimates is equal to or greater than 0.07.4 Columns (7) reports the adjusted R2 for the augmented regressions. The R2 s suggest that regressors in the augmented regressions have strong predictive ability on future stock returns.

5

Conclusions

This paper demonstrates that a European prime business cycle indicator, namely ELEI, predicts European stock returns both in-sample and out-of-sample. The predictive power of ELEI is above and beyond that contained in CLEI. Thus, we provide a direct line linking return predictability to economic fundamentals. Our analysis also sheds light on the integration of European stock markets. While our study focuses on the stock market, it will be of interest to investigate the predictive ability of ELEI in the bond market, commodity market, currency market.

References [1] Artis, M.K, 1997. Classical business cycles for G-7 and European countries. Journal of Business 70, 249–279. 4

We also run in-sample regressions by including the country’s own dividend yield and short-term interest rate in equation (11). The empirical analysis still indicates that ELEI is usually significant and displays stronger predictive power than CLEI. These results are reported in an online appendix.

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[2] Artis, M.K., Krolzig, H-M., and Toro, J., 2004. The European business cycle. Oxford Economic Papers 56, 1-44. [3] Balvers, R., Cosimano, T., and McDonald, T., 1990. Predicting stock returns in an efficient market. Journal of Finance 45, 1109–1118. [4] Campbell, J., and Thompson, S., 2008. Predicting the equity premium out of sample: Can anything beat historical average? Review of Financial Studies 21, 1509-1531. [5] Clark, T.E., and West, K.D., 2007. Approximately normal tests for equal predictive accuracy in nested models. Journal of Econometrics 138, 291-311. [6] Fama, E.F., 1990. Stock return, expected returns, and real activity. Journal of Finance 45, 1089-1108. [7] Fama, E.F., and French, K., 1989,. Business conditions and expected returns on stocks and bonds. Journal of Financial Economics 25, 23-49. [8] Giacomini, R., Rossi, B., 2010. Forecast comparisons in unstable environments. Journal of Applied Econometrics 25, 595–620. [9] Harvey, C.R., 1991. The world price of covariance risk. Journal of Finance 46, 111-157. [10] Huang, D., and Zhou, G., 2013. Economic and market conditions: Two state variables that predict the stock market. Working Paper. [11] Harvey, D.I., Leybourne, S.J. and Newbold, P., 1998. Tests for forecast encompassing. Journal of Business and Economic Statistics 16, 254–59. [12] Ilmanen, A., 1995. Time-varying expected returns in international bond markets. Journal of Finance 50, 481-506.

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[13] Keim, D., and Stambaugh, R., 1986. Predicting returns in the stock and bond markets. Journal of Financial Economics 17, 357-390. [14] Kose, M.A., Otrok, C., and Whiteman, C.H., 2003. International business cycles: World, region, and country-specific factors. American Economic Review 93, 12161239. [15] Merton, R., 1973. An intertemporal capital asset pricing model. Econometrica 41, 867-887. [16] Schwert, G.W., 1990. Stock returns and real activity: A century of evidence. Journal of Finance 1990 45, 1237-57. [17] Welch, I., and Goyal, A., 2008. A comprehensive look at the empirical performance of equity premium prediction. Review of Financial Studies 21, 1455-1508. [18] Zhou, G., and Zhu, X., 2014. What drives the international bond risk premia? Working Paper. [19] Zhu, X., 2013. Perpetual learning and stock return predictability. Economics Letters 121, 19-22.

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Table 1: Summary Statistics of International Stock Returns Country Austria Belgium Denmark France Germany Italy

Mean 0.30 0.50 0.90 0.62 0.54 0.59

Std.dev 6.76 5.64 5.43 5.75 6.12 6.91

min max Country Mean -36.5 24.8 Netherlands 0.63 -35.3 22.8 Norway 0.55 -19.6 17.0 Spain 0.66 -24.8 19.9 Sweden 1.14 -28.7 18.0 Swiss 0.59 -19.9 24.1 UK 0.65

Std.dev min max 5.37 -25.6 15.7 7.19 -35.5 18.3 6.42 -29.5 23.5 6.82 -24.5 29.7 4.70 -26.6 13.0 4.72 -30.3 13.4

The table report summary statistics for monthly national currency stock returns (in percent) for the European countries. Data are from Datastream. The sample period is 1980:01-2013:07.

Table 2: Out-of-sample Forecasting Results Country Austria Belgium Denmark France Germany Italy Netherlands Norway Spain Sweden Swiss UK

(1) 2 ROS (%) 0.059∗∗∗ 0.023∗ 0.041∗∗∗ 0.045∗∗∗ 0.033∗∗∗ 0.029∗∗ 0.052∗∗∗ 0.085∗∗∗ 0.013∗∗ 0.039∗∗∗ 0.063∗∗∗ 0.027∗∗

(2) ∆(%) -0.56 -0.28 0.07 -0.07 -0.15 -0.58 -0.08 -0.19 -0.05 0.11 0.30 0.12

(3) 2 ROS (%) 0.086∗∗∗ 0.079∗∗∗ 0.073∗∗∗ 0.082∗∗∗ 0.065∗∗∗ 0.073∗∗∗ 0.087∗∗∗ 0.075∗∗∗ 0.035∗∗∗ 0.047∗∗∗ 0.066∗∗∗ 0.050∗∗∗

(4) ∆(%) 0.62 0.11 0.10 0.65 0.63 0.08 0.64 0.87 0.43 0.95 0.78 0.35

(5) M HLN 0.96 1.00 0.02 1.00 1.00 1.00 0.00 0.00 0.15 0.07 0.00 0.99

The table reports the out-of-sample R2 statistics for international stock returns over the 1990:01-2013:07 forecast evaluation period. Utility gain (∆) is the portfolio management fee (in annualized percentage return) that an investor with mean-variance preferences and risk aversion coefficient of three would be willing to pay to have access to the forecasting model. For computing utility gain, the weight on stocks in the investor’s portfolio is restricted to lie between zero and 1.5. Statistical significance for the out-of-sample R2 is based on the p-value for the Clark and West (2007) out-of-sample MSPE-adjusted statistic. ∗ , ∗∗ , and ∗∗∗ indicate significance at the 10%, 5%, and 1% levels, respectively. Column (5) reports p-values for the MHLN statstic applied to the 1990:01-2013:07 out-of-sample forecasts. 12

Table 3: In-sample Forecasting Results Country Austria Belgium Denmark France Germany Italy Netherlands Norway Spain Sweden Swiss UK

(1) b β CLEI -0.12∗∗∗ -0.07∗∗∗ -0.08∗∗∗ -0.09∗∗∗ -0.06∗∗∗ -0.07∗∗∗ -0.07∗∗∗ -0.12∗∗∗ -0.07∗∗∗ -0.09∗∗∗ -0.06∗∗∗ -0.04∗∗∗

(2) R2 0.077 0.042 0.083 0.048 0.044 0.031 0.076 0.093 0.021 0.084 0.093 0.027

(3) b β ELEI -0.12∗∗∗ -0.10∗∗∗ -0.10∗∗∗ -0.09∗∗∗ -0.10∗∗∗ -0.10∗∗∗ -0.09∗∗∗ -0.12∗∗∗ -0.08∗∗∗ -0.11∗∗∗ -0.07∗∗∗ -0.07∗∗∗

(4) R2 0.097 0.084 0.085 0.056 0.052 0.045 0.085 0.096 0.045 0.079 0.075 0.050

(5) b β CLEI -0.05 0.01 -0.03∗∗ -0.04 -0.01 -0.01 -0.02 -0.07∗∗ -0.03 -0.06∗∗∗ -0.04∗∗∗ -0.00

(6) b β ELEI -0.09∗∗∗ -0.10∗∗ -0.07∗ -0.08∗∗∗ -0.09∗∗ -0.09∗∗∗ -0.08∗∗∗ -0.07∗ -0.07∗∗ -0.08 -0.02 -0.07∗∗∗

(7) R2 0.112 0.085 0.092 0.059 0.053 0.047 0.087 0.115 0.046 0.108 0.103 0.052

The table respectively reports the empirical results for the predictive regression models ri,t+1 = α + β CLEI CLEIt + εi,t (columns 1 and 2), ri,t+1 = α + β ELEI ELEIt + εi,t (columns 3 and 4), and ri,t+1 = α + β CLEI CLEIt + β ELEI ELEIt + εi,t (columns 5, 6, and 7). The sample period is 1980:01-2013:07. ∗ , ∗∗ , and ∗∗∗ indicate significance at the 10%, 5%, and 1% levels, respectively.

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Figure 1: Fluctuation test statistics. The …gure plots the two-sided Fluctuation test statistics (Giacomini and Rossi, 2010) and the 5% and 10% critical values of the Fluctuation test. The length of the rolling window is 10 years.

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