Non-parametric estimation of a time varying GARCH model

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acf acf acf acf 0.0 0.4 0.8 0.0 0.4 0.8 0.0 0.4 0.8 0.0 0.4 0.8 0 5 10 20 30 INR/USD 0 5 10 20 30 CNY/EURO 0 5 10 20 30 RUB/EURO 0 5 10 20 30 Dow Jones acf acf acf acf 0.0 0.4 0.8 0.0 0.4 0.8 0.0 0.4 0.8 0.0 0.4 0.8 0 5 10 20 30 INR/EURO 0 5 10 20 30 BRL/USD 0 5 10 20 30 RND/EURO 0 5 10 20 30 Figure 2: Autocorrelation functions of the squared returns 36 BSE acf acf acf acf 0.0 0.4 0.8 0.0 0.4 0.8 0.0 0.4 0.8 0.0 0.4 0.8 0 5 10 20 30 CNY/USD 0 5 10 20 30 BRL/EURO 0 5 10 20 30 S & P 500 0 5 10 20 30 NSE
volatility volatility 0 10 20 30 0 10 20 30 0 500 1000 2000 tvGARCH 0 500 1000 2000 EGARCH volatility volatility 0 10 20 30 0 10 20 30 0 500 1000 2000 FIGARCH 0 500 1000 2000 GARCH Figure 3: In sample volatility forecasts for the BRL/EURO data 37
Page 1 and 2: Non-parametric estimation of a time
Page 3 and 4: 1 Introduction The first decade of
Page 5 and 6: have been discussed in Section 2. S
Page 7 and 8: Under Assumption 1(i), (3) is a sta
Page 9 and 10: The estimator of αi(u0) as a solut
Page 11 and 12: 4 Asymptotic results Towards provin
Page 13 and 14: Notations. bj = bj(u0) = Bias(ˆαj
Page 15 and 16: This problem is under investigation
Page 17 and 18: provides insight into the nature of
Page 19 and 20: Proof of Proposition 2.3. We can wr
Page 21 and 22: Now consider n� 1 nh k=p+1 (uk
Page 23 and 24: ⎡ X ⊤ ⎢ 1 W1 ⎢ ⎣ and usin
Page 25 and 26: Hence the result can be easily prov
Page 27 and 28: The variance expression given in Th
Page 29 and 30: (iii) a GJR process if where ω,α,
Page 31 and 32: 31 Table 1: Summary statistics of t
Page 33 and 34: 33 Table 3: Aggregated mean squared
Page 35: −1.5 0.0 1.0 −2 −1 0 1 −1.0

Non-parametric estimation of a time varying GARCH model

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