{"id":99053,"date":"2023-11-21T01:14:15","date_gmt":"2023-11-21T01:14:15","guid":{"rendered":"https:\/\/science-hub.click\/%E3%82%A2%E3%83%AB%E3%83%9E-%E5%AE%9A%E7%BE%A9\/"},"modified":"2023-11-21T01:14:15","modified_gmt":"2023-11-21T01:14:15","slug":"%E3%82%A2%E3%83%AB%E3%83%9E-%E5%AE%9A%E7%BE%A9","status":"publish","type":"post","link":"https:\/\/science-hub.click\/?p=99053","title":{"rendered":"\u30a2\u30eb\u30de – \u5b9a\u7fa9"},"content":{"rendered":"

\u5c0e\u5165<\/h2>

\u7d71\u8a08\u5b66\u3067\u306f\u3001 ARMA<\/b>\u30e2\u30c7\u30eb (\u81ea\u5df1\u56de\u5e30\u30e2\u30c7\u30eb\u304a\u3088\u3073\u79fb\u52d5\u5e73\u5747<\/i>\u30e2\u30c7\u30eb)\u3001\u307e\u305f\u306fBox-Jenkins \u30e2\u30c7\u30eb<\/b>\u304c\u4e3b\u8981\u306a\u6642\u7cfb\u5217\u30e2\u30c7\u30eb\u3067\u3059\u3002<\/p>

\u6642\u7cfb\u5217X<\/i> t<\/i><\/sub>\u304c\u4e0e\u3048\u3089\u308c\u305f\u5834\u5408\u3001 ARMA<\/a><\/span>\u30e2\u30c7\u30eb\u306f\u3001\u3053\u306e\u7cfb\u5217\u306e\u5c06\u6765\u306e\u5024\u3092\u7406\u89e3\u3057\u3001\u5834\u5408\u306b\u3088\u3063\u3066\u306f\u4e88\u6e2c\u3059\u308b\u305f\u3081\u306e\u30c4\u30fc\u30eb<\/a><\/span>\u3067\u3059\u3002\u30e2\u30c7\u30eb\u306f\u3001\u81ea\u5df1\u56de\u5e30\u90e8\u5206 (AR) \u3068\u79fb\u52d5\u5e73\u5747\u90e8\u5206 (MA) \u306e 2 \u3064\u306e\u90e8\u5206\u3067\u69cb\u6210\u3055\u308c\u307e\u3059\u3002\u30e2\u30c7\u30eb\u306f\u4e00\u822c\u306b ARMA( p<\/i> , q<\/i> ) \u3067\u8868\u3055\u308c\u307e\u3059\u3002\u3053\u3053\u3067\u3001 p \u306f<\/i>AR \u90e8\u5206\u306e\u6b21\u6570\u3001 q \u306f<\/i>MA \u90e8\u5206\u306e\u6b21\u6570\u3067\u3059\u3002<\/p>

\n\"\u30a2\u30eb\u30de<\/figure>

\u81ea\u5df1\u56de\u5e30\u30e2\u30c7\u30eb<\/h2>

AR( p<\/i> ) \u3068\u3044\u3046\u8868\u8a18\u306f\u3001\u6b21\u6570p<\/i>\u306e\u81ea\u5df1\u56de\u5e30\u30e2\u30c7\u30eb\u3092\u6307\u3057\u307e\u3059\u3002 AR( p<\/i> ) \u30e2\u30c7\u30eb\u306b\u6ce8\u76ee<\/p>

$$ { X_t = c + \\sum_{i=1}^p \\varphi_i X_{t-i}+ \\varepsilon_t .\\,} $$<\/div><\/dd><\/dl>

\u307e\u305f\u306f

$$ {\\varphi_1, \\ldots, \\varphi_p} $$<\/div>\u306f\u30e2\u30c7\u30eb\u30d1\u30e9\u30e1\u30fc\u30bf<\/b><\/i>\u3067\u3042\u308a\u3001\u5b9a\u6570\u3067\u3042\u308a<\/i><\/span>\u3001
$$ {\\varepsilon_t} $$<\/div>\u30db\u30ef\u30a4\u30c8\u30ce\u30a4\u30ba\u3002\u5b9a\u6570\u306f\u6587\u732e\u3067\u306f\u7701\u7565\u3055\u308c\u308b\u3053\u3068\u304c\u3088\u304f\u3042\u308a\u307e\u3059\u3002<\/p>

\u5b9a\u5e38\u6027\u3092\u4fdd\u8a3c\u3059\u308b\u306b\u306f\u3001\u30d1\u30e9\u30e1\u30fc\u30bf\u306b\u5bfe\u3059\u308b\u8ffd\u52a0\u306e\u5236\u7d04\u304c\u5fc5\u8981\u3067\u3059\u3002\u305f\u3068\u3048\u3070\u3001AR(1) \u30e2\u30c7\u30eb\u306e\u5834\u5408\u3001\u6b21\u306e\u3088\u3046\u306a\u30d7\u30ed\u30bb\u30b9\u304c\u5b9f\u884c\u3055\u308c\u307e\u3059\u3002 \u03c61<\/i> |<\/sub> \u2265 1 \u306f\u9759\u6b62\u3057\u3066\u3044\u307e\u305b\u3093\u3002<\/p>

\n\"\u30a2\u30eb\u30de<\/figure>

\u4f8b: AR(1) \u30d7\u30ed\u30bb\u30b9<\/span><\/h3>

AR(1) \u30e2\u30c7\u30eb\u306f\u6b21\u306e\u3088\u3046\u306b\u4e0e\u3048\u3089\u308c\u307e\u3059\u3002 <\/p>

$$ {X_t = c + \\varphi X_{t-1}+\\varepsilon_t,\\,} $$<\/div><\/dd><\/dl>

\u307e\u305f\u306f

$$ {\\varepsilon_t} $$<\/div>\u306f\u3001\u30bc\u30ed\u5e73\u5747<\/a><\/span>\u3068\u5206\u6563<\/a><\/span>\u03c3 2 \u3092<\/sup><\/span>\u6301\u3064\u30db\u30ef\u30a4\u30c8 \u30ce\u30a4\u30ba\u3067\u3059\u3002\u6b21\u306e\u5834\u5408\u3001\u30e2\u30c7\u30eb\u306f\u5206\u6563\u5b9a\u5e38\u3067\u3059\u3002
$$ {|\\varphi|<1} $$<\/div> \u3002\u3082\u3057
$$ {\\varphi=1} $$<\/div>\u306e\u5834\u5408\u3001\u30d7\u30ed\u30bb\u30b9\u306f\u5358\u4f4d<\/span>\u6839<\/span>\u3092\u793a\u3057\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u305d\u308c\u304c\u30e9\u30f3\u30c0\u30e0 \u30a6\u30a9\u30fc\u30af<\/a><\/span>\u3067\u3042\u308a\u3001\u5206\u6563\u304c\u5b9a\u5e38\u3067\u306f\u306a\u3044\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002\u305d\u308c\u3067\u3001\u4eee\u5b9a\u3057\u3066\u304f\u3060\u3055\u3044
$$ {|\\varphi|<1} $$<\/div> \u3001\u5e73\u5747\u03bc<\/span>\u306b\u6ce8\u76ee\u3059\u308b\u3068\u3001\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002 <\/p>
$$ {\\mbox{E}(X_t)=\\mbox{E}(c)+\\varphi\\mbox{E}(X_{t-1})+\\mbox{E}(\\varepsilon_t)\\Rightarrow \\mu=c+\\varphi\\mu+0.} $$<\/div><\/dd><\/dl>

\u305d\u308c\u3067<\/p>

$$ {\\mu=\\frac{c}{1-\\varphi}.} $$<\/div><\/dd><\/dl>

\u7279\u306b\u3001 c<\/i> = 0<\/span>\u3068\u3059\u308b\u3053\u3068\u306f\u3001\u5e73\u5747\u304c\u30bc\u30ed\u306b\u306a\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002<\/p>

\u5dee\u7570\u306f<\/p>

$$ {\\textrm{var}(X_t)=E(X_t^2)-\\mu^2=\\frac{\\sigma^2}{1-\\varphi^2}.} $$<\/div><\/dd><\/dl>

\u81ea\u5df1\u5171\u5206\u6563\u95a2\u6570\u306f\u6b21\u306e\u3088\u3046\u306b\u4e0e\u3048\u3089\u308c\u307e\u3059\u3002 <\/p>

$$ {B_n=E(X_{t+n}X_t)-\\mu^2=\\frac{\\sigma^2}{1-\\varphi^2}\\,\\,\\varphi^{|n|}.} $$<\/div><\/dd><\/dl>

\u81ea\u5df1\u5171\u5206\u6563\u95a2\u6570\u304c\u6b21\u306e\u5272\u5408\u3067\u6e1b\u5c11\u3059\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002

$$ {\\tau=-1\/\\ln(\\varphi)} $$<\/div> \u3002<\/p>

\u30d1\u30ef\u30fc<\/a><\/span>\u30b9\u30da\u30af\u30c8\u30eb\u5bc6\u5ea6\u306f<\/a><\/span>\u3001\u81ea\u5df1\u5171\u5206\u6563\u95a2\u6570\u306e\u30d5\u30fc\u30ea\u30a8\u5909\u63db<\/span>\u3067\u3059\u3002\u96e2\u6563\u7684\u306a\u5834\u5408\u3001\u3053\u308c\u306f\u6b21\u306e\u3088\u3046\u306b\u66f8\u304b\u308c\u307e\u3059\u3002 <\/p>

$$ {\\Phi(\\omega)= \\frac{1}{\\sqrt{2\\pi}}\\,\\sum_{n=-\\infty}^\\infty B_n e^{-i\\omega n} =\\frac{1}{\\sqrt{2\\pi}}\\,\\left(\\frac{\\sigma^2}{1+\\varphi^2-2\\varphi\\cos(\\omega)}\\right). } $$<\/div><\/dd><\/dl>

\u5206\u6bcd\u306b\u30b3\u30b5\u30a4\u30f3<\/a><\/span>\u9805\u304c\u5b58\u5728\u3059\u308b\u305f\u3081\u3001\u3053\u306e\u5c55\u958b\u306f\u5468\u671f\u7684\u3067\u3059\u3002\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0<\/a><\/span>\u6642\u9593<\/a><\/span>( \u0394t<\/i> = 1<\/span> ) \u304c\u6e1b\u8870\u6642\u9593<\/i>( \u03c4<\/span> ) \u3088\u308a\u5c0f\u3055\u3044\u3068\u4eee\u5b9a\u3059\u308b\u3068\u3001 Bn<\/i>\u306e<\/i><\/sub><\/span>\u9023\u7d9a\u8fd1\u4f3c<\/a><\/span>\u3092\u4f7f\u7528\u3067\u304d\u307e\u3059\u3002 <\/p>

$$ {B(t)\\approx \\frac{\\sigma^2}{1-\\varphi^2}\\,\\,\\varphi^{|t|}} $$<\/div><\/dd><\/dl>

\u3053\u308c\u306f\u30b9\u30da\u30af\u30c8\u30eb\u5bc6\u5ea6\u306e\u30ed\u30fc\u30ec\u30f3\u30c4\u5f62\u5f0f\u3092\u793a\u3057\u307e\u3059\u3002 <\/p>

$$ {\\Phi(\\omega)= \\frac{1}{\\sqrt{2\\pi}}\\,\\frac{\\sigma^2}{1-\\varphi^2}\\,\\frac{\\gamma}{\\pi(\\gamma^2+\\omega^2)}} $$<\/div><\/dd><\/dl>

\u3053\u3053\u3067\u3001 \u03b3 = 1 \/ \u03c4 \u306f\u3001<\/span> \u03c4<\/span>\u306b\u95a2\u9023\u4ed8\u3051\u3089\u308c\u305f\u89d2\u5468\u6ce2\u6570<\/span>\u3067\u3059\u3002<\/p>

X<\/i> t<\/i><\/sub><\/span>\u306e\u5225\u306e\u5f0f\u306f\u3001\u4ee5\u4e0b\u3092\u4ee3\u5165\u3059\u308b\u3053\u3068\u3067\u5c0e\u51fa\u3055\u308c<\/a><\/span>\u307e\u3059<\/i><\/sub>\u3002<\/i><\/span>

$$ {c+\\varphi X_{t-2}+\\varepsilon_{t-1}} $$<\/div>\u5b9a\u7fa9\u5f0f\u3067\u306f\u3002\u3053\u306e\u64cd\u4f5c\u3092N<\/i>\u56de\u7d9a\u3051\u308b\u3068\u3001 <\/p>
$$ {X_t=c\\sum_{k=0}^{N-1}\\varphi^k+\\varphi^NX_{t-N}+\\sum_{k=0}^{N-1}\\varphi^k\\varepsilon_{t-k}.} $$<\/div><\/dd><\/dl>

N \u304c<\/i>\u975e\u5e38\u306b\u5927\u304d\u304f\u306a\u308b\u3068\u3001

$$ {\\varphi^N} $$<\/div> 0 \u306b\u8fd1\u3065\u304d\u3001\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002 <\/p>
$$ {X_t=\\frac{c}{1-\\varphi}+\\sum_{k=0}^\\infty\\varphi^k\\varepsilon_{t-k}.} $$<\/div><\/dd><\/dl>

X<\/i> t \u306f<\/i><\/sub><\/span>\u539f\u5b50\u6838\u3068\u7573\u307f\u8fbc\u307e\u308c\u305f\u30db\u30ef\u30a4\u30c8 \u30ce\u30a4\u30ba\u3067\u3042\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002

$$ {\\varphi^k} $$<\/div>\u4e00\u5b9a\u306e\u5e73\u5747\u3092\u52a0\u3048\u307e\u3059\u3002\u30db\u30ef\u30a4\u30c8 \u30ce\u30a4\u30ba\u304c\u30ac\u30a6\u30b9\u306e\u5834\u5408\u3001 X<\/i> t<\/i><\/sub><\/span>\u3082\u901a\u5e38\u306e\u30d7\u30ed\u30bb\u30b9\u3067\u3059\u3002\u4ed6\u306e\u5834\u5408\u306b\u306f\u3001\u4e2d\u5fc3\u6975\u9650\u5b9a\u7406\u306f\u3001<\/a><\/span>\u6b21\u306e\u5834\u5408\u306bX<\/i> t<\/i><\/sub><\/span>\u304c\u307b\u307c\u6b63\u898f\u306b\u306a\u308b\u3053\u3068\u3092\u793a\u3057\u307e\u3059\u3002
$$ {\\varphi} $$<\/div>\u7d71\u4e00\u306b\u8fd1\u3044\u3067\u3059\u3002<\/p>

AR\u30d1\u30e9\u30e1\u30fc\u30bf\u306e\u63a8\u5b9a<\/span><\/h3>

AR( p<\/i> ) \u30e2\u30c7\u30eb\u306f\u6b21\u306e\u3088\u3046\u306b\u4e0e\u3048\u3089\u308c\u307e\u3059\u3002 <\/p>

$$ { X_t = \\sum_{i=1}^p \\varphi_i X_{t-i}+ \\varepsilon_t.\\,} $$<\/div><\/dd><\/dl>

\u63a8\u5b9a\u3059\u308b\u30d1\u30e9\u30e1\u30fc\u30bf\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002

$$ {\\varphi_i} $$<\/div>\u3053\u3053\u3067\u3001 i<\/i> = 1, …, p \u3067\u3059<\/i>\u3002\u3053\u308c\u3089\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u3068\u5171\u5206\u6563<\/a><\/span>\u95a2\u6570 (\u3057\u305f\u304c\u3063\u3066\u81ea\u5df1\u76f8\u95a2) \u306e\u9593\u306b\u306f\u76f4\u63a5\u306e\u5bfe\u5fdc\u95a2\u4fc2<\/a><\/span>\u304c\u3042\u308a\u3001\u3053\u308c\u3089\u306e\u95a2\u4fc2\u3092\u53cd\u8ee2\u3059\u308b\u3053\u3068\u3067\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u3092\u5c0e\u304d\u51fa\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u3053\u308c\u3089\u306f\u30e6\u30fc\u30eb\u30fb\u30a6\u30a9\u30fc\u30ab\u30fc\u65b9\u7a0b\u5f0f<\/b>\u3067\u3059: <\/p>
$$ { \\gamma_m = \\sum_{k=1}^p \\varphi_k \\gamma_{m-k} + \\sigma_\\varepsilon^2\\delta_m } $$<\/div><\/dd><\/dl>

\u3053\u3053\u3067\u3001 m<\/i> = 0, …, p<\/i> \u3001\u3053\u308c\u306f\u3059\u3079\u3066\u306e<\/a><\/span>p<\/i> + 1 \u65b9\u7a0b\u5f0f\u3067\u5f97\u3089\u308c\u307e\u3059\u3002\u4fc2\u6570\u03b3 m \u306f<\/i><\/sub><\/span>X<\/i>\u306e\u81ea\u5df1\u76f8\u95a2\u95a2\u6570\u3067\u3059\u3002

$$ {\\sigma_\\varepsilon} $$<\/div>\u306f\u30db\u30ef\u30a4\u30c8\u30ce\u30a4\u30ba\u306e\u504f\u5dee\uff08\u6a19\u6e96\u504f\u5dee\uff09\u3001\u03b4 m \u306f<\/sub>\u30af\u30ed\u30cd\u30c3\u30ab\u30fc\u8a18\u53f7<\/a><\/span>\u3067\u3059\u3002<\/p>

m<\/i> = 0 \u306e\u5834\u5408\u3001\u65b9\u7a0b\u5f0f\u306e\u6700\u5f8c\u306e\u90e8\u5206\u306f\u30bc\u30ed\u4ee5\u5916\u306b\u306a\u308a\u307e\u3059\u3002 m<\/i> > 0 \u3092\u3068\u308b\u3068\u3001\u524d\u306e\u5f0f\u306f\u884c\u5217\u30b7\u30b9\u30c6\u30e0\u3068\u3057\u3066\u8a18\u8ff0\u3055\u308c\u307e\u3059\u3002 <\/p>

$$ {\\begin{bmatrix} \\gamma_1 \\\\ \\gamma_2 \\\\ \\gamma_3 \\\\ \\vdots \\\\ \\end{bmatrix} = \\begin{bmatrix} \\gamma_0 & \\gamma_{-1} & \\gamma_{-2} & \\dots \\\\ \\gamma_1 & \\gamma_0 & \\gamma_{-1} & \\dots \\\\ \\gamma_2 & \\gamma_{1} & \\gamma_{0} & \\dots \\\\ \\vdots & \\vdots & \\vdots & \\ddots \\\\ \\end{bmatrix} \\begin{bmatrix} \\varphi_{1} \\\\ \\varphi_{2} \\\\ \\varphi_{3} \\\\ \\vdots \\\\ \\end{bmatrix} } $$<\/div><\/dd><\/dl>

m<\/i> = 0 \u306e\u5834\u5408\u3001\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002 <\/p>

$$ { \\gamma_0 = \\sum_{k=1}^p \\varphi_k \\gamma_{-k} + \\sigma_\\varepsilon^2 } $$<\/div><\/dd><\/dl>

\u3053\u308c\u306b\u3088\u308a\u3001\u898b\u3064\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059

$$ {\\sigma_\\varepsilon^2} $$<\/div> \u3002<\/p>

\u30e6\u30fc\u30eb \u30a6\u30a9\u30fc\u30ab\u30fc\u65b9\u7a0b\u5f0f\u306f\u3001\u7406\u8ad6\u4e0a\u306e\u5171\u5206\u6563\u3092\u63a8\u5b9a\u5024\u306b\u7f6e\u304d\u63db\u3048\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u30e2\u30c7\u30eb \u30d1\u30e9\u30e1\u30fc\u30bf\u30fc AR( p<\/i> ) \u3092\u63a8\u5b9a\u3059\u308b\u624b\u6bb5\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u5024\u3092\u53d6\u5f97\u3059\u308b 1 \u3064\u306e\u65b9\u6cd5\u306f\u3001\u6700\u521d\u306ep<\/i>\u30e9\u30b0\u306b\u95a2\u3059\u308bX<\/i> t<\/i><\/sub>\u306e\u7dda\u5f62\u56de\u5e30<\/a><\/span>\u3092\u8003\u616e\u3059\u308b\u3053\u3068\u3067\u3059\u3002<\/p>

\n\"\u30a2\u30eb\u30de<\/figure>

\u30e6\u30fc\u30eb\u30fb\u30a6\u30a9\u30fc\u30ab\u30fc\u65b9\u7a0b\u5f0f\u306e\u53d6\u5f97<\/span><\/h4>

AR \u30d7\u30ed\u30bb\u30b9\u306e\u5b9a\u7fa9\u5f0f\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002 <\/p>

$$ { X_t = \\sum_{i=1}^p \\varphi_i\\,X_{t-i}+ \\varepsilon_t.\\,} $$<\/div><\/dd><\/dl>

\u4e21\u8fba\u306bX<\/i> t<\/i> \u2212 m<\/i><\/sub>\u3092\u639b\u3051\u3066\u671f\u5f85\u5024\u3092\u53d6\u308b\u3068\u3001\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002 <\/p>

$$ {E[X_t X_{t-m}] = E\\left[\\sum_{i=1}^p \\varphi_i\\,X_{t-i} X_{t-m}\\right]+ E[\\varepsilon_t X_{t-m}].} $$<\/div><\/dd><\/dl>

\u3055\u3066\u3001\u81ea\u5df1\u76f8\u95a2\u95a2\u6570\u306e\u5b9a\u7fa9<\/a><\/span>\u306b\u3088\u308a\u3001E[ X<\/i> t<\/i><\/sub> X<\/i> t<\/i> \u2212 m<\/i><\/sub> ] = \u03b3 m<\/i><\/sub>\u3067\u3042\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002\u30db\u30ef\u30a4\u30c8 \u30ce\u30a4\u30ba\u9805\u306f\u4e92\u3044\u306b\u72ec\u7acb\u3057\u3066\u304a\u308a\u3001\u3055\u3089\u306b\u3001 X<\/i> t<\/i> \u2212 m<\/i>\u306f<\/sub>\u03b5 t<\/sub>\u304b\u3089\u72ec\u7acb\u3057\u3066\u3044\u307e\u3059\u3002\u3053\u3053\u3067\u3001 m \u306f<\/i>0<\/a><\/span>\u3088\u308a\u5927\u304d\u304f\u306a\u308a\u307e\u3059\u3002 m<\/i> > 0 \u306e\u5834\u5408\u3001E[\u03b5 t<\/i><\/sub> X<\/i> t<\/i> \u2212 m<\/i><\/sub> ] = 0\u3002m<\/i> = 0 \u306e\u5834\u5408\u3001 <\/p>

$$ {E[\\varepsilon_t X_{t}] = E\\left[\\varepsilon_t \\left(\\sum_{i=1}^p \\varphi_i\\,X_{t-i}+ \\varepsilon_t\\right)\\right] = \\sum_{i=1}^p \\varphi_i\\, E[\\varepsilon_t\\,X_{t-i}] + E[\\varepsilon_t^2] = 0 + \\sigma_\\varepsilon^2, } $$<\/div><\/dd><\/dl>

\u3055\u3066\u3001 m<\/i> \u2265 0 \u306e\u5834\u5408\u3001 <\/p>

$$ {\\gamma_m = E\\left[\\sum_{i=1}^p \\varphi_i\\,X_{t-i} X_{t-m}\\right] + \\sigma_\\varepsilon^2 \\delta_m.} $$<\/div><\/dd><\/dl>

\u3055\u3089\u306b\u3001 <\/p>

$$ {E\\left[\\sum_{i=1}^p \\varphi_i\\,X_{t-i} X_{t-m}\\right] = \\sum_{i=1}^p \\varphi_i\\,E[X_{t} X_{t-m+i}] = \\sum_{i=1}^p \\varphi_i\\,\\gamma_{m-i}, } $$<\/div><\/dd><\/dl>

\u3053\u308c\u306b\u3088\u308a\u3001\u30e6\u30fc\u30eb\u30fb\u30a6\u30a9\u30fc\u30ab\u30fc\u65b9\u7a0b\u5f0f\u304c\u5f97\u3089\u308c\u307e\u3059\u3002 <\/p>

$$ {\\gamma_m = \\sum_{i=1}^p \\varphi_i \\gamma_{m-i} + \\sigma_\\varepsilon^2 \\delta_m.} $$<\/div><\/dd><\/dl>

m<\/i> \u2265 0 \u306e\u5834\u5408\u3002m<\/i> < 0 \u306e\u5834\u5408\u3001 <\/p>

$$ {\\gamma_m = \\gamma_{-m} = \\sum_{i=1}^p \\varphi_i \\gamma_{|m|-i} + \\sigma_\\varepsilon^2 \\delta_m.} $$<\/div><\/dd><\/dl><\/div>

\u53c2\u8003\u8cc7\u6599<\/h2>
  1. Arma \u2013 cebuano<\/a><\/li>
  2. Arma \u2013 tch\u00e8que<\/a><\/li>
  3. Arma \u2013 allemand<\/a><\/li>
  4. Arma \u2013 anglais<\/a><\/li>
  5. Arma (desambiguaci\u00f3n) \u2013 espagnol<\/a><\/li>
  6. Arma (argipen) \u2013 basque<\/a><\/li><\/ol><\/div>\n
    \n

    \n \u30a2\u30eb\u30de – \u5b9a\u7fa9\u30fb\u95a2\u9023\u52d5\u753b\n <\/h2>\n
    \n \n
    \n
    \n