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hahnbeelee committed Dec 12, 2023
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50 changes: 25 additions & 25 deletions nbs/docs/models/ARCH.ipynb
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"source": [
"### Return Series\n",
"\n",
"Since the 1970s, the financial industry has been very prosperous with advancement of computer and Internet technology. Trade of financial products (including various derivatives) generates a huge amount of data which form financial time series. For finance, the return on a financial product is most interesting, and so our attention focuses on the return series. If {Pt } is the closing price at time t for a certain financial product, then the return on this product is\n",
"Since the 1970s, the financial industry has been very prosperous with advancement of computer and Internet technology. Trade of financial products (including various derivatives) generates a huge amount of data which form financial time series. For finance, the return on a financial product is most interesting, and so our attention focuses on the return series. If \\{Pt } is the closing price at time t for a certain financial product, then the return on this product is\n",
"\n",
"$$X_t = \\frac{(P_t − P_{t−1})}{P_{t−1}} ≈ log(P_t ) − log(P_{t−1}).$$\n",
"\n",
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2 changes: 1 addition & 1 deletion nbs/src/core/models.ipynb
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" \n",
" $$\\sigma_t^2 = w + \\sum_{i=1}^p a_i y_{t-i}^2 + \\sum_{j=1}^q b_j \\sigma_{t-j}^2$$. \n",
" \n",
" Here {$v_t$} is a sequence of iid random variables with zero mean and unit variance. \n",
" Here \\{$v_t$} is a sequence of iid random variables with zero mean and unit variance. \n",
" The coefficients $w$, $a_i$, $i=1,...,p$, and $b_j$, $j=1,...,q$ must satisfy the following conditions: \n",
" \n",
" 1. $w > 0$ and $a_i, b_j \\geq 0$ for all $i$ and $j$. \n",
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