HAR-RV Deep Dive

Heterogeneous Autoregressive Realised Volatility decomposes RV persistence into three trader horizons: daily (HFT), weekly (dealers), and monthly (institutions).

Σβ (persistence)

0.900

Ann. vol (avg)

0.0%

Daily share

Monthly share

Realised Volatility Path (annualised %)

Horizon Decomposition — average RV contribution per trader horizon

ACF of Realised Volatility — long-memory decay

β_d (daily)0.36

β_w (weekly)0.30

β_m (monthly)0.24

ω (constant)0.000025

Noise intensity0.15

Observations750

Seed11

RV_{t + 1}^{(d)} = ω + β_{d} RV_{t}^{(d)} + β_{w} \overline{RV}_{t}^{(w)} + β_{m} \overline{RV}_{t}^{(m)} + ε_{t + 1}

\overline{RV}_{t}^{(w)} = \frac{1}{5} k = 1 \sum 5 RV_{t - k + 1}; \overline{RV}_{t}^{(m)} = \frac{1}{22} k = 1 \sum 22 RV_{t - k + 1}

Set β_m large to see the monthly (institutional) component dominate — ACF decay slows significantly. Reduce β_d+β_w+β_m below 1 to keep stationarity. The three-horizon structure parsimoniously captures long-memory volatility without fractional integration.

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