Forecasting volatility: EWMA, GARCH and HAR

Wednesday 8 Apr 2026. Nifty rose 3.78% and closed at 23,997.35. That evening the twenty session realised volatility read 29.46 and the 30 day at the money implied volatility read 17.56, both percent a year. Twenty sessions later, on 8 May 2026, the realised volatility of the sessions that followed came in at 13.45. Two numbers on one evening, both answers to "how wild will the next month be", and the next month came in at less than half of one of them. My habit with any volatility forecast is to ask three things before I trust it: what horizon, scored against what, and how often it misses by a gap like this one. Everything below comes from NSE end of day files, dated, nothing live and nothing a view on the next month.

The idea, plainly

What does a volatility forecast actually forecast?

Volatility is never seen, only returns. One return says little about the distribution behind it: a big move can come from a calm distribution. So a forecast has two jobs, to average squared returns sensibly and to say where volatility heads when no news arrives. Two facts shape every model. Volatility clusters, because big days follow big days. And it mean reverts towards a long run level, though not on a schedule.

The models below are four steps on one ladder. The last two need a fit to history. The first two need only a choice, and that choice is where most of the damage is done.

Why does an equal weight window fail?

In a twenty session window every return carries the same weight, 5.00 percent of the variance, until the day it leaves and drops to nothing. A forecast should not move because a day aged out. EWMA, the exponentially weighted moving average, fades the weights by a fixed factor each day, the decay. At 0.94, today's return gets 6.00 percent.

Update:
s2(t) = L*s2(t-1)
      + (1-L)*r(t)^2
Weight on r(t-k):
  (1-L) * L^k
Example, L = 0.94
prior variance 0.81 (%^2)
today's return 2.5%
s2 = 0.94*0.81 + 0.06*6.25
   = 1.1364
Daily s.d. 1.07%;
annual: times sqrt(252)

Where does GARCH add something?

EWMA forecasts flat. GARCH, the generalised autoregressive conditional heteroscedasticity model, adds a small constant that pulls variance towards a long run level, so a forecast made from a spike declines and one made from a lull rises. Everything turns on persistence: the weights on yesterday's estimate and on today's squared return, added up. At 0.97 the gap to the long run level shrinks by that factor every day.

s2(t) = w + a*r(t-1)^2
      + b*s2(t-1)
Persistence p = a + b < 1
Long run V = w/(1-a-b)
k days ahead:
  V + p^k * (s2(t)-V)
Example: w = 0.02,
a = 0.08, b = 0.89
p = 0.97, V = 0.02/0.03
  = 0.667 (daily %^2)
20 day forecast: the mean
of the k day values,
k = 1 to 20

What does HAR do differently?

HAR, the heterogeneous autoregressive model, drops the latent variance and regresses the next period's realised volatility on three averages: yesterday, the last week and the last month. Different market users look at different horizons, a day trader at the day and a fund at the month, and their reactions stack into something that looks like long memory. It is a plain regression, easy to fit and easy to read.

RV(t+1) = c + bd*RVd
        + bw*RVw + bm*RVm
RVd: yesterday
RVw: mean of last 5 sessions
RVm: mean of last 22
Fit: ordinary least squares

Worked example: eight dates, one scorecard

How do you score a forecast?

Fix a start date and make the forecast from data up to that close. Wait, then measure the realised volatility of the next twenty sessions, with the same horizon, estimator and factor. The error is forecast less realised. Never score a model on the sample it was fitted on, because it has already seen the answer.

A second caution: start dates a day apart share nineteen of their twenty returns, so a hundred scored dates are not a hundred independent tests.

What do eight dates show?

I picked eight start dates spread across the file and scored two simple forecasts: the trailing twenty session realised volatility held flat, and the 30 day implied volatility, the market's own price for the same stretch. Four each. Both missed badly at the start of stress: on 6 Mar 2026 implied read 18.10 and the next twenty sessions came in at 29.46.

The common mistake

The claim: Fit a GARCH model and you know next month's volatility. A fitted model gives a number, with a tidy fit statistic, and that is the trap. The table above scored two forecasts on eight dates and each missed by 11.36 points or more at least once, on 8 Apr 2026 for trailing (29.46 against 13.45) and on 6 Mar 2026 for implied (18.10 against 29.46). A model that fades a spike also misses when the spike turns out to be a regime. A forecast is a point on a distribution of outcomes. State the horizon, score it on dates it has not seen, and treat the miss as part of the answer.

Key takeaways

• A window drops a day with a bang; EWMA lets the weight fade.
• GARCH adds a pull towards a long run level, set by persistence.
• HAR regresses on day, week and month averages of realised volatility.
• Score each forecast against the realised volatility of the same horizon.
• Neighbouring start dates overlap, so scored dates are not independent tests.
• A model must beat trailing and implied volatility, not zero.

Before you trade. Derivatives trading carries a high risk of loss. SEBI's study "Profitability of Individual Traders in the Equity Derivatives Segment (FY25 to FY26)" (August 2026) found that 87.7% of individual traders in equity F&O made net losses in FY26, with aggregate net losses of Rs 91,685 crore. Read the SEBI study