# Time-Varying Window Length for Correlation Forecasts

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## Abstract

**:**

## 1. Introduction

## 2. Data

## 3. Model

#### 3.1. Submodels

#### 3.2. Combining Submodels

#### 3.3. Model Uncertainty

#### 3.4. Forecasts

## 4. Results

#### 4.1. Model Comparisons

#### 4.2. Submodel Probability Distributions

#### 4.3. Time-Varying Window Length

#### 4.4. Time-Varying Window Model

## 5. Robustness

#### 5.1. Model Comparison with Alternative Metrics

#### 5.2. Long-Horizon Forecasting

#### 5.3. Alternative Forecasting Methods

## 6. Concluding Comments

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Appendix A. Estimation

#### Appendix A.1. Deriving Forecasts

#### Appendix A.2. Priors

## Appendix B. Forecasts

## References

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1. | Early papers related to our application include: (Andersen et al. 2003; Andersen et al. 2005; Andreou and Ghysels 2002; Barndorff-Nielsen and Shephard 2002; Maheu and McCurdy 2002; Martnes et al. 2004; Liu and Maheu 2009). |

2. | |

3. | |

4. | For example: (Pastor and Stambaugh 2012; Diris 2014). |

5. | See: Andreou and Ghysels (2002) in volatility; Liu and Maheu (2008) in realized volatility; Maheu and Gordon (2008) in macroeconomic variables; and Maheu and McCurdy (2009) in market return distributions. |

6. | The COMEX gold futures (GC) intra-day prices are missing for June 2011 in the raw data. We have thus disregarded this period in the empirical analysis of the paper. |

7. | Recall that, under the null of their construction, the realized measures are time-additive. |

**Figure 1.**Daily realized correlations for three futures contracts, April 2007–February 2015. Plots are the daily realized correlation measures for three futures contracts labelled as SP, GC and CL. These daily series are computed using a 15-min grid of changes in log futures prices from TickData beginning 2 April 2007 and ending 17 February 2015.

**Figure 2.**QQ-plot of FisRCorr (Fisher-transformed Realized Correlation), April 2007–February 2015. QQ-plots of Fisher transformed daily realized correlation measures for three futures contracts labelled as SP, GC and CL. These daily series are computed using a 15-min grid of changes in log futures prices from TickData beginning 2 April 2007 and ending 17 February 2015.

**Figure 3.**Monthly S&P logRV Forecasts, 1885–2013. In each plot, the forecasts for monthly logRV from two alternative models are compared to realized logRV for the period 1885–2013. The top plot compares how well the equally-weighted expanding-window forecasts track the one-month-ahead realized logRV as compared to the forecasts from the equally-weighted moving-average model, which uses the past five years of observations. The middle plot compares the ${M}_{*}$ model’s (time-varying weights) forecasts to the one-month-ahead realized logRV. The bottom plot is the same as the middle plot, except that we use a higher prior for lambda, the probability of model change.

**Figure 4.**Daily FisRCorr (SP, GC) forecasts, April 2007–February 2015. In each plot, the forecasts for daily FisRCorr (SP, GC) from two alternative models are compared to realized FisRCorr (SP, GC) for the period 2 April 2007–17 February 2015. The top plot compares how well the equally-weighted expanding-window forecasts track the one-day-ahead realized FisRCorr (SP, GC) as compared to the forecasts from the equally-weighted moving-average model, which uses the past 60 days of observations. The bottom plot compares the ${M}_{*}$ model’s (time-varying weights) forecasts to the one-day-ahead realized FisRCorr (SP, GC).

**Figure 5.**Submodel probabilities over time: monthly logRV. The top panel shows the 3D-plot of the submodel probabilities over time with a new submodel being introduced every 12 months. The bottom panel plots are submodel probabilities over time associated with specific submodels for monthly logRV forecasts.

**Figure 6.**Time-varying window length for monthly logRV and daily FisRCorr. The time-varying window length (${W}_{t}^{*}$) for monthly logRV and for three series of daily FisRCorr are plotted on the Y-axes; units are in number of months and days, respectively.

Symbol | Mean | Variance | Skewness | Kurtosis |
---|---|---|---|---|

Panel A: Summary Statistics for Realized Variances | ||||

Monthly Frequency, Sample Period 1885–2013 | ||||

logRV (S&P) | −6.5229 | 0.9012 | 0.7168 | 4.1608 |

RV (S&P) | 0.0026 | 2.45E-05 | 6.2809 | 54.4785 |

Daily Frequency, Sample Period April 2007–February 2015 | ||||

logRV (SP) | −10.3408 | 1.7155 | 0.3836 | 3.8697 |

logRV (GC) | −10.6170 | 1.4464 | 0.2023 | 3.3387 |

logRV (CL) | −9.1946 | 1.4406 | 0.2025 | 3.3763 |

RV (SP) | 9.34E-05 | 7.91E-08 | 9.2736 | 118.6787 |

RV (GC) | 5.51E-05 | 2.03E-08 | 14.8284 | 325.9368 |

RV (CL) | 2.23E-04 | 1.86E-07 | 6.0766 | 57.7090 |

Panel B: Summary Statistics of Realized Correlations | ||||

Daily Frequency, Sample Period April 2007–February 2015 | ||||

FisRCorr (SP, GC) | 0.1806 | 0.1656 | −0.0773 | 2.6457 |

FisRCorr (SP, CL) | 0.3398 | 0.1438 | −0.2480 | 2.9505 |

FisRCorr (GC, CL) | 0.3338 | 0.1288 | −0.0292 | 2.8818 |

RCorr (SP, GC) | 0.1570 | 0.1255 | −0.2723 | 2.2468 |

RCorr (SP, CL) | 0.2952 | 0.1011 | −0.6201 | 2.8742 |

RCorr (GC, CL) | 0.2912 | 0.0904 | −0.4602 | 2.6393 |

Expanding Window (${\mathit{M}}_{\mathbf{1}}$) | Constant Window (${\mathit{M}}_{\mathbf{t}\mathbf{-}\mathbf{60}}$) | Time-Varying Weights (${\mathit{M}}_{\mathbf{*}}$) | |
---|---|---|---|

Panel A: Monthly Frequency, Sample Period 1885–2013 | |||

Intercept | −4.6094 | −1.9388 | −0.2893 |

(−3.50) *** | (−7.11) *** | (−1.25) | |

Slope | 0.2906 | 0.7014 | 0.9574 |

(−3.55) *** | (−7.19) *** | (−1.21) | |

R^{2} | 0.14% | 16.14% | 33.21% |

Panel B: Daily Frequency, Sample Period April 2007–February 2015 | |||

logRV (SP) | |||

Intercept | −3.5967 | −1.1799 | −0.5597 |

(−4.14) *** | (−4.69) *** | (−2.46) ** | |

Slope | 0.6682 | 0.8855 | 0.9482 |

(−4.11) *** | (−4.73) *** | (−2.36) ** | |

R^{2} | 3.34% | 40.21% | 48.44% |

logRV (GC) | |||

Intercept | 3.9854 | −1.2219 | −0.6585 |

(2.68) *** | (−3.43) *** | (−1.83) * | |

Slope | 1.4097 | 0.8856 | 0.9426 |

(2.86) *** | (−3.41) *** | (−1.69) * | |

R^{2} | 4.64% | 25.99% | 27.85% |

logRV (CL) | |||

Intercept | 6.4257 | −0.4784 | −0.0078 |

(6.83) *** | (−2.27) ** | (−0.04) | |

Slope | 1.7750 | 0.9466 | 1.0012 |

(7.25) *** | (−2.34) ** | (0.05) | |

R^{2} | 12.18% | 46.50% | 49.14% |

^{2}associated with these forecast regressions indicates the proportion of variability in the out-of-sample realized variable that is predicted by the forecasts.

Expanding Window (${\mathit{M}}_{\mathbf{1}}$) | Constant Window (${\mathit{M}}_{\mathit{t}\mathbf{-}\mathbf{60}}$) | Time-Varying Weights (${\mathit{M}}_{\mathbf{*}}$) | Time-Varying Weights (Higher $\mathit{\lambda}$ Prior) | |
---|---|---|---|---|

FisRCorr (SP, GC) | ||||

Intercept | 0.0865 | 0.0274 | −0.0125 | −0.0125 |

(2.50) ** | (2.77) *** | (−1.37) | (−1.38) | |

Slope | 0.4787 | 0.8247 | 1.0121 | 1.0169 |

(−3.06) *** | (−5.53) *** | (0.41) | (0.58) | |

R^{2} | 0.40% | 25.83% | 38.15% | 38.50% |

FisRCorr (SP, CL) | ||||

Intercept | 0.1726 | 0.0414 | −0.0076 | −0.0146 |

(8.26) *** | (3.63) *** | (−0.67) | (−1.30) | |

Slope | 0.6240 | 0.8844 | 1.0006 | 1.0180 |

(−5.26) *** | (−4.28) *** | (0.02) | (0.68) | |

R^{2} | 3.77% | 35.49% | 42.26% | 43.55% |

FisRCorr (GC, CL) | ||||

Intercept | −0.5591 | 0.0585 | −0.0118 | −0.0168 |

(−5.98) *** | (4.03) *** | (−0.85) | (−1.21) | |

Slope | 2.2142 | 0.8092 | 0.9963 | 1.0215 |

(5.26) *** | (−5.17) *** | (−0.11) | (0.61) | |

R^{2} | 4.51% | 19.79% | 29.21% | 30.16% |

^{2}associated with these forecast regressions indicates the proportion of variability in the out-of-sample realized variable that is predicted by the forecasts.

Expanding Window (${\mathit{M}}_{\mathbf{1}}$) | Constant Window (${\mathit{M}}_{\mathit{t}\mathbf{-}\mathbf{60}}$) | Time-Varying Weights (${\mathit{M}}_{\mathbf{*}}$) | Time-Varying Weights (Higher $\mathit{\lambda}$ Prior) | |
---|---|---|---|---|

Panel A: Monthly Frequency, Sample Period 1885–2013 | ||||

log(ML): logRV (S&P) | −2043.01 | −1929.67 | −1742.83 | −1714.76 |

Panel B: Daily Frequency, Sample Period April 2007–February 2015 | ||||

log(ML): FisRCorr (SP, GC) | −1023.83 | −703.28 | −542.52 | −514.54 |

log(ML): FisRCorr (SP, CL) | −892.03 | −411.52 | −345.85 | −311.43 |

log(ML): FisRCorr (GC, CL) | −776.67 | −528.84 | −418.49 | −400.80 |

Symbol | Mean | Std. Dev. | Skewness | Kurtosis |
---|---|---|---|---|

Panel A: Monthly Frequency, Sample Period 1885–2013 | ||||

logRV (S&P) | 23.60 | 10.98 | 0.907 | 3.797 |

Panel B: Daily Frequency, Sample Period April 2007–February 2015 | ||||

FisRCorr (SP, GC) | 68.47 | 54.46 | 1.489 | 4.757 |

FisRCorr (SP, CL) | 66.60 | 36.75 | 0.741 | 3.101 |

FisRCorr (GC, CL) | 87.69 | 55.88 | 1.176 | 4.599 |

Panel A: Cross-Sectional Characteristics | ||||
---|---|---|---|---|

W* | Characteristics of Correlation Time-Series | |||

Symbol | Mean | Standard Deviation | AR(1) Coefficient | AR(2) Coefficient |

Daily Frequency, Sample Period April 2007–February 2015 | ||||

FisRCorr (SP, GC) | 68.47 | 0.4069 | 0.5570 | 0.5200 |

FisRCorr (SP, CL) | 66.60 | 0.3792 | 0.5690 | 0.5372 |

FisRCorr (GC, CL) | 87.69 | 0.3589 | 0.4202 | 0.3964 |

Panel B: Time-Series Regression on VIX | ||||

Symbol | Intercept | VIX | R^{2} | N |

Daily Frequency, Sample Period April 2007–February 2015 | ||||

FisRCorr(SP,GC) | 110.8256 | −1.9169 | 13.25% | 1949 |

(40.86) *** | (−17.24) *** | |||

FisRCorr(SP,CL) | 88.6728 | −0.9988 | 7.90% | 1949 |

(47.02) *** | (−12.92) *** | |||

FisRCorr(GC,CL) | 146.98 | −2.6829 | 24.64% | 1949 |

(56.66) *** | (−25.23) *** |

Time-Varying Weights (${\mathit{M}}_{*}$) | Time-Varying Window (${\mathit{M}}_{{\mathit{W}}^{*}}$) | |
---|---|---|

Panel A: Monthly Frequency, Sample Period 1885–2013 | ||

logRV (S&P) | ||

Intercept | −0.2893 | −0.7724 |

(−1.25) | (−4.11) *** | |

Slope | 0.9574 | 0.8835 |

(−1.21) | (−4.06) *** | |

R^{2} | 33.21% | 39.00% |

log(ML ) | −1714.76 | −1778.72 |

Panel B: Daily Frequency, Sample Period April 2007–February 2015 | ||

FisRCorr (SP, GC) | ||

Intercept | −0.0125 | −0.0027 |

(−1.37) | (−0.31) | |

Slope | 1.0121 | 0.9507 |

(0.41) | (−1.91) * | |

R^{2} | 38.15% | 41.17% |

log(ML) | −514.54 | −524.53 |

FisRCorr (SP, CL) | ||

Intercept | −0.0076 | 0.0056 |

(−0.67) | (0.53) | |

Slope | 1.0006 | 0.9634 |

(0.02) | (−1.53) | |

R^{2} | 42.26% | 45.38% |

log(ML) | −311.43 | −298.23 |

FisRCorr (GC, CL) | ||

Intercept | −0.0118 | 0.0143 |

(−0.85) | (1.11) | |

Slope | 0.9963 | 0.9263 |

(−0.11) | (−2.34) ** | |

R^{2} | 29.21% | 30.16% |

log(ML) | −400.80 | −404.22 |

^{2}associated with the Mincer–Zarnowitz regressions indicates the proportion of variability in the out-of-sample realized variable that is predicted by the forecasts.

Expanding Window (${\mathit{M}}_{\mathbf{1}}$) | Constant Window (${\mathit{M}}_{\mathbf{t}-\mathbf{60}}$) | Time-Varying Weights (${\mathit{M}}_{*}$) | Time-Varying Window (${\mathit{M}}_{{\mathit{W}}^{*}}$) | |
---|---|---|---|---|

Panel A: Monthly Frequency, Sample Period 1885–2013 | ||||

logRV (S&P) | ||||

MAE | 0.7230 | 0.6723 | 0.5986 | 0.5740 |

avg. SSE | 0.9012 | 0.7568 | 0.6027 | 0.5505 |

Panel B: Daily Frequency, Sample Period April 2007–February 2015 | ||||

FisRCorr (SP, GC) | ||||

MAE | 0.3319 | 0.2749 | 0.2500 | 0.2430 |

avg. SSE | 0.1649 | 0.1228 | 0.1024 | 0.0974 |

FisRCorr (SP, CL) | ||||

MAE | 0.2987 | 0.2366 | 0.2263 | 0.2201 |

avg. SSE | 0.1383 | 0.0927 | 0.0830 | 0.0785 |

FisRCorr (GC, CL) | ||||

MAE | 0.2784 | 0.2490 | 0.2339 | 0.2314 |

avg.SSE | 0.1229 | 0.1032 | 0.0911 | 0.0892 |

Expanding Window (${\mathit{M}}_{\mathbf{1}}$) | Constant Window (${\mathit{M}}_{\mathit{t}-\mathbf{60}}$) | Time-Varying Weights (${\mathit{M}}_{*}$) | Expanding Window (${\mathit{M}}_{\mathbf{1}}$) | Constant Window (${\mathit{M}}_{\mathit{t}-\mathbf{60}}$) | Time-Varying Weights (${\mathit{M}}_{*}$) | |
---|---|---|---|---|---|---|

Panel A: Monthly Frequency, Sample Period 1885–2013 | ||||||

logRV(S&P) | ||||||

Intercept | −11.7138 | −4.4630 | −4.2274 | |||

(−2.58) *** | (−4.17) *** | (−5.09) *** | ||||

Slope | -0.7887 | 0.3134 | 0.3506 | |||

(−2.60) *** | (−4.23) *** | (−5.38) *** | ||||

R^{2} | 3.30% | 9.99% | 18.57% | |||

Panel B: Daily Frequency, Sample Period April 2007–February 2015 | ||||||

logRV (SP) | FisRCorr (SP, GC) | |||||

Intercept | −7.9923 | −3.1354 | −3.7217 | 0.2784 | 0.0909 | 0.0784 |

(−2.00) ** | (−2.68) *** | (−3.88) *** | (1.57) | (1.50) | (1.63) | |

Slope | 0.2309 | 0.6957 | 0.6409 | −0.4652 | 0.4907 | 0.5364 |

(−1.95) * | (−2.86) *** | (−4.08) *** | (−1.80) * | (−2.90) *** | (−3.32) *** | |

R^{2} | 0.78% | 49.02% | 52.65% | 1.00% | 22.78% | 33.15% |

logRV (GC) | FisRCorr (SP, CL) | |||||

Intercept | −2.0881 | −3.1775 | −3.4293 | 0.2426 | 0.1218 | 0.1060 |

(−0.28) | (−2.22) ** | (−3.05) *** | (1.65) * | (1.46) | (1.63) | |

Slope | 0.8229 | 0.7010 | 0.6787 | 0.3888 | 0.6604 | 0.6872 |

(−0.25) | (−2.26) ** | (−3.07) *** | (−1.32) | (−1.95) * | (−2.30) ** | |

R^{2} | 4.53% | 48.90% | 53.14% | 3.32% | 45.20% | 52.74% |

logRV (CL) | FisRCorr (GC, CL) | |||||

Intercept | 5.0959 | −1.7683 | −1.5729 | 0.0456 | 0.1597 | 0.1490 |

(0.84) | (−1.18) | (−1.19) | (0.09) | (2.27) ** | (2.58) *** | |

Slope | 1.6283 | 0.8072 | 0.8299 | 0.7226 | 0.5127 | 0.5356 |

(0.91) | (−1.22) | (−1.22) | (−0.22) | (−2.84) ** | (−3.32) *** | |

R^{2} | 18.13% | 64.29% | 67.59% | 1.44% | 24.94% | 32.40% |

^{2}associated with these forecast regressions indicates the proportion of variability in the out-of-sample realized variable that is predicted by the forecasts.

**Table 10.**Forecast regression results for the exponentially-weighted moving-average (ExpWMA) method.

Expanding Window (${\mathit{M}}_{\mathbf{1}}$) | Constant Window (${\mathit{M}}_{\mathit{t}-\mathbf{60}}$) | Time-Varying Window (${\mathit{M}}_{{\mathit{W}}^{*}}$) | Expanding Window (${\mathit{M}}_{\mathbf{1}}$) | Constant Window (${\mathit{M}}_{\mathit{t}-\mathbf{60}}$) | Time-Varying Window (${\mathit{M}}_{{\mathit{W}}^{*}}$) | |
---|---|---|---|---|---|---|

Panel A: Monthly Frequency, Sample Period 1885–2013 | ||||||

logRV(S&P) | ||||||

Intercept | −0.3687 | −0.8555 | −0.7179 | |||

(−1.31) | (−3.46) *** | (−3.92) ** | ||||

Slope | 0.9414 | 0.8677 | 0.8915 | |||

(−1.37) | (−3.51) *** | (−3.88) *** | ||||

R^{2} | 24.62% | 26.33% | 40.65% | |||

Panel B: Daily Frequency, Sample Period April 2007–February 2015 | ||||||

logRV (SP) | FisRCorr (SP, GC) | |||||

Intercept | −0.2745 | −0.3506 | −0.8070 | 0.0044 | 0.0068 | 0.0057 |

(−1.26) | (−1.62) | (−4.23) *** | (0.50) | (0.78) | (0.69) | |

Slope | 0.9734 | 0.9660 | 0.9234 | 0.9616 | 0.9495 | 0.9417 |

(−1.27) | (−1.63) | (−4.17) *** | (−1.41) | (−1.89) * | (−2.38) ** | |

R^{2} | 51.98% | 52.09% | 55.97% | 39.16% | 39.34% | 43.28% |

logRV (GC) | FisRCorr (SP, CL) | |||||

Intercept | −0.5998 | −0.6796 | −0.8829 | 0.0137 | 0.0159 | 0.0119 |

(−1.81) * | (−2.07) ** | (−2.82) *** | (1.31) | (1.53) | (1.18) | |

Slope | 0.9440 | 0.9364 | 0.9183 | 0.9629 | 0.9559 | 0.9554 |

(−1.79) * | (−2.06) ** | (−2.77) *** | (−1.52) | (−1.83) * | (−1.95) * | |

R^{2} | 31.49% | 31.55% | 32.87% | 44.41% | 44.55% | 47.11% |

logRV (CL) | FisRCorr (GC, CL) | |||||

Intercept | −0.1723 | −0.2160 | −0.3162 | 0.0157 | 0.0200 | 0.0230 |

(−0.88) | (−1.12) | (−1.68) * | (1.22) | (1.58) | (1.91) * | |

Slope | 0.9804 | 0.9757 | 0.9663 | 0.9436 | 0.9314 | 0.9182 |

(−0.93) | (−1.16) | (−1.66) * | (−1.74) * | (−2.15) ** | (−2.77) *** | |

R^{2} | 52.09% | 52.22% | 53.19% | 30.44% | 30.53% | 33.11% |

^{2}associated with these forecast regressions indicates the proportion of variability in the out-of-sample realized variable that is predicted by the forecasts.

Expanding Window (${\mathit{M}}_{\mathbf{1}}$) | Constant Window (${\mathit{M}}_{\mathit{t}-\mathbf{60}}$) | Time-Varying Window (${\mathit{M}}_{{\mathit{W}}^{*}}$) | Expanding Window (${\mathit{M}}_{\mathbf{1}}$) | Constant Window (${\mathit{M}}_{\mathit{t}-\mathbf{60}}$) | Time-Varying Window (${\mathit{M}}_{{\mathit{W}}^{*}}$) | |
---|---|---|---|---|---|---|

Panel A: Monthly Frequency, Sample Period 1885–2013 | ||||||

logRV(S&P) | ||||||

Intercept | 0.1959 | −0.3810 | −1.1933 | |||

(0.96) | (−2.12) ** | (−7.37) *** | ||||

Slope | 1.0257 | 0.9424 | 0.8183 | |||

(0.83) | (−2.10) ** | (−7.36) *** | ||||

R^{2} | 42.72% | 44.33% | 42.58% | |||

Panel B: Daily Frequency, Sample Period April 2007–February 2015 | ||||||

logRV(SP) | FisRCorr(SP,GC) | |||||

Intercept | −0.4016 | −0.6282 | −1.1191 | −0.0107 | 0.0054 | 0.0030 |

(−1.86) * | (−3.28) *** | (−6.28) *** | (−1.07) | (0.63) | (0.36) | |

Slope | 0.9662 | 0.9406 | 0.8932 | 1.0062 | 0.9354 | 0.9277 |

(−1.61) | (−3.22) *** | (−6.22) *** | (0.18) | (−2.46) ** | (−3.00) *** | |

R^{2} | 51.69% | 56.63% | 57.69% | 31.08% | 39.57% | 42.99% |

logRV(GC) | FisRCorr(SP,CL) | |||||

Intercept | −0.3448 | −1.2086 | −1.5986 | 0.0426 | 0.0098 | 0.0210 |

(−0.76) | (−3.70) *** | (−5.29) *** | (3.55) *** | (0.94) | (2.08) ** | |

Slope | 0.9801 | 0.8874 | 0.8516 | 0.9403 | 0.9572 | 0.9235 |

(−0.46) | (−3.66) *** | (−5.21) *** | (−1.95) * | (−1.78) * | (−3.36) *** | |

R^{2} | 20.67% | 29.56% | 31.06% | 32.56% | 44.82% | 45.81% |

logRV(CL) | FisRCorr(GC,CL) | |||||

Intercept | 1.1764 | −0.2740 | −0.2449 | −0.0685 | 0.0290 | 0.0253 |

(3.99) *** | (−1.33) | (−1.23) | (−3.38) *** | (2.20) ** | (2.04) ** | |

Slope | 1.1495 | 0.9690 | 0.9738 | 1.0744 | 0.8924 | 0.8949 |

(4.59) *** | (−1.40) | (−1.22) | (1.47) | (−3.28) *** | (−3.47) *** | |

R^{2} | 38.48% | 48.93% | 50.66% | 18.84% | 27.49% | 31.00% |

^{2}associated with these forecast regressions indicates the proportion of variability in the out-of-sample realized variable that is predicted by the forecasts.

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Jeon, Y.; McCurdy, T.H.
Time-Varying Window Length for Correlation Forecasts. *Econometrics* **2017**, *5*, 54.
https://doi.org/10.3390/econometrics5040054

**AMA Style**

Jeon Y, McCurdy TH.
Time-Varying Window Length for Correlation Forecasts. *Econometrics*. 2017; 5(4):54.
https://doi.org/10.3390/econometrics5040054

**Chicago/Turabian Style**

Jeon, Yoontae, and Thomas H. McCurdy.
2017. "Time-Varying Window Length for Correlation Forecasts" *Econometrics* 5, no. 4: 54.
https://doi.org/10.3390/econometrics5040054