US Dollar to Indian Rupee Zero Slope Spline-GARCH Volatility Analysis
High-persistence model: shocks decay very slowly, so the theoretical long-run value may not be practically meaningful
Volatility prediction for Friday, October 23rd, 2026
1 Day
4.69%
decreased by 0.36%
1 Week
4.71%
decreased by 0.34%
1 Month
4.77%
decreased by 0.28%
Analysis last updated: Thursday, October 22, 2026 at 08:08 PM UTC
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How returns affect tomorrow's volatilityVolatility Forecast
How volatility evolves over timeParameter Estimates
May 30, 1990 to Oct 16, 2026Model Insight
With persistence 1.000, volatility shocks have a half-life of 11748 trading days (~46.6 years), close to a unit root, so long-run forecasts are highly sensitive to this estimate.
τ
Zero Slope Spline-GARCH Model
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High persistence: persistence 1.000, shock half-life ~11748 days
| Param | Value | t-stat |
|---|---|---|
| ωconst | 0.8055 | 0.65 |
| αARCH | 0.1520 | 1.37 |
| βGARCH | 0.8480 | 7.79*** |
Spline Coefficients
K=10
| γ1 | 0.2160 | 0.18 |
| γ2 | -0.3686 | -0.31 |
| γ3 | 0.1635 | 1.45 |
| γ4 | -0.0051 | -0.06 |
| γ5 | 0.0001 | 0.00 |
| γ6 | -0.0446 | -0.95 |
| γ7 | 0.0590 | 1.60 |
| γ8 | -0.0065 | -0.16 |
| γ9 | -0.0696 | -1.43 |
| γ10 | 0.1003 | 2.43** |
1.000
Persistence11748d
Half-lifeτ
Zero Slope Spline-GARCH Model
Tap to view equation
| Parameter | Value | t-statistic |
|---|---|---|
ω const Unconditional variance weight | 0.8055 | 0.65 |
α ARCH Response to squared shocks | 0.1520 | 1.37 |
β GARCH Volatility persistence | 0.8480 | 7.79*** |
Spline Coefficients
K=10
| γ1 | 0.2160 | 0.18 |
| γ2 | -0.3686 | -0.31 |
| γ3 | 0.1635 | 1.45 |
| γ4 | -0.0051 | -0.06 |
| γ5 | 0.0001 | 0.00 |
| γ6 | -0.0446 | -0.95 |
| γ7 | 0.0590 | 1.60 |
| γ8 | -0.0065 | -0.16 |
| γ9 | -0.0696 | -1.43 |
| γ10 | 0.1003 | 2.43** |
Persistence:
1.000
Half-life:
11748 days
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