\u307e\u305a\u3001ewm\u306f\u3053\u306e\u3088\u3046\u306a\u5f62\u3067\u4f7f\u3046\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n
import pandas as pd\nimport numpy as np\na = [1, 2, 3, np.nan, 5, 6]\ndf = pd.DataFrame(a)\ndf.head(6)<\/code><\/pre><\/div>\n\n\n\n<\/p>\n\n\n\n
\u7d50\u679c\uff1a\n\t0\n0\t1.0\n1\t2.0\n2\t3.0\n3\tNaN\n4\t5.0\n5\t6.0<\/code><\/pre><\/div>\n\n\n\n\u6307\u6570\u8377\u91cd\u8a08\u7b97\u306e\u4f8b<\/p>\n\n\n\n
df.ewm(com=2).mean()<\/code><\/pre><\/div>\n\n\n\n\u7d50\u679c\uff1a\n 0\n0\t1.000000\n1\t1.600000\n2\t2.263158\n3\t2.263158\n4\t3.675159\n5\t4.689408<\/code><\/pre><\/div>\n\n\n\n <\/strong><\/p>\n\n\n\n\u3053\u306e\u3088\u3046\u306bewm\u3092\u7528\u3044\u308b\u3053\u3068\u3067\u904e\u53bb\u306e\u5024\u306b\u91cd\u307f\u3065\u3051\u3057\u306a\u304c\u3089\u73fe\u5728\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306e\u5024\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002<\/p>\n\n\n\n
\u4ee5\u4e0b\u3067\u3001\u30aa\u30d7\u30b7\u30e7\u30f3\u30d1\u30e9\u30e1\u30fc\u30bf\u306e\u8a2d\u5b9a\u306b\u3088\u308b\u8a08\u7b97\u65b9\u6cd5\u306e\u9055\u3044\u306b\u3064\u3044\u3066\u8aac\u660e\u3057\u307e\u3059\u3002<\/p>\n\n\n\n
<\/span>\u5e73\u6ed1\u5316\u4fc2\u6570(alpha)<\/span><\/h2>\n\n\n\n\u5e73\u6ed1\u5316\u4fc2\u6570\u3067\u3042\u308b\\(\\alpha\\)\u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5\u3068\u3057\u3066\u306fewm\u306e\u30aa\u30d7\u30b7\u30e7\u30f3\u306bcom, span, hallife\u3092\u305d\u308c\u305e\u308c\u8a2d\u5b9a\u3059\u308b\u3053\u3068\u3067\u7570\u306a\u308b\u8a08\u7b97\u5f0f\u3067\u6c42\u3081\u308b\u3053\u3068\u304c\u53ef\u80fd\u3067\u3059\u3002<\/p>\n\n\n\n
<\/span>com\u3092\u4f7f\u7528\u3059\u308b\u5834\u5408<\/span><\/h3>\n\n\n\n\\(\\alpha = \\frac{1}{1+com}\\) \u3068\u306a\u308a\u307e\u3059\u3002com\u306f0\u4ee5\u4e0a\u306e\u5024\u3092\u8a2d\u5b9a\u3057\u307e\u3059\u3002<\/p>\n\n\n\n
\u4f8b\uff1a<\/p>\n\n\n\n
df.ewm(com=4).mean()<\/code><\/pre><\/div>\n\n\n\n\u7d50\u679c\uff1a\n 0\n0\t1.000000\n1\t1.555556\n2\t2.147541\n3\t2.147541\n4\t3.261087\n5\t4.159303<\/code><\/pre><\/div>\n\n\n\n<\/span>span\u3092\u4f7f\u7528\u3059\u308b\u5834\u5408<\/span><\/h3>\n\n\n\n\\(\\alpha = \\frac{2}{1+span}\\)\u3068\u306a\u308a\u307e\u3059\u3002span\u306f0\u4ee5\u4e0a\u306e\u5024\u3092\u8a2d\u5b9a\u3057\u307e\u3059\u3002<\/p>\n\n\n\n
\u4f8b\uff1a<\/p>\n\n\n\n
df.ewm(span=4).mean()<\/code><\/pre><\/div>\n\n\n\n\u7d50\u679c\uff1a\n\t0\n0\t1.000000\n1\t1.625000\n2\t2.326531\n3\t2.326531\n4\t3.893996\n5\t4.934841<\/code><\/pre><\/div>\n\n\n\n<\/span>hallife\u3092\u4f7f\u7528\u3059\u308b\u5834\u5408<\/span><\/h3>\n\n\n\n\\(\\alpha =1 – \\exp(\\frac{-\\ln{2}}{halflife})\\)<\/p>\n\n\n\n
df.ewm(halflife=4).mean()<\/code><\/pre><\/div>\n\n\n\n\u7d50\u679c\uff1a\n\t0\n0\t1.000000\n1\t1.543214\n2\t2.114950\n3\t2.114950\n4\t3.144696\n5\t3.995515<\/code><\/pre><\/div>\n\n\n\n<\/span>\u5e73\u6ed1\u5316\u5e73\u5747\u306e\u8a08\u7b97\u65b9\u6cd5(adjutst)<\/span><\/h2>\n\n\n\n\u6307\u6570\u52a0\u91cd\u5e73\u5747\u306e\u8a08\u7b97\u7d50\u679c\u3067\u3042\u308b\\(y_t\\)\u3092\u3001\u6c42\u3081\u308b\u65b9\u6cd5\u306b\u6e1b\u8870\u3092\u52a0\u3048\u3066\u8abf\u6574\u3059\u308b\u304b\u3057\u306a\u3044\u304b\u3092\u9078\u629e\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u30c7\u30d5\u30a9\u30eb\u30c8\u306f\u8abf\u6574\u3059\u308b(adjust=True)\u3068\u306a\u3063\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n
<\/span>adjust=True\u306e\u5834\u5408<\/span><\/h3>\n\n\n\n\\(y_t = \\frac{x_t+(1-\\alpha)x_{t-1}+(1-\\alpha^2)x_{t-2}…+(1-\\alpha)^tx_0}{1+(1-\\alpha)+(1-\\alpha)^2+…+(1-\\alpha)^t}\\)<\/p>\n\n\n\n
df.ewm(span=4, adjust=True).mean()<\/code><\/pre><\/div>\n\n\n\n\u7d50\u679c\uff1a\n 0\n0\t1.000000\n1\t1.625000\n2\t2.326531\n3\t2.326531\n4\t3.893996\n5\t4.934841<\/code><\/pre><\/div>\n\n\n\n<\/span>adjust=Flase\u306e\u5834\u5408<\/span><\/h3>\n\n\n\nadjus=False\u3068\u3057\u305f\u5834\u5408\u306f\u3088\u308a\u30b7\u30f3\u30d7\u30eb\u306a\u4ee5\u4e0b\u306e\u8a08\u7b97\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n
\\( y_t = (1-\\alpha)y_{t-1} + \\alpha x_t \\)<\/p>\n\n\n\n
\u3053\u3053\u3067\u3001\\(y_0 = x_0\\)\u3067\u3059\u3002<\/p>\n\n\n\n
df.ewm(span=4, adjust=False).mean()<\/code><\/pre><\/div>\n\n\n\n\t0\n0\t1.000000\n1\t1.400000\n2\t2.040000\n3\t2.040000\n4\t3.597895\n5\t4.558737<\/code><\/pre><\/div>\n\n\n\n<\/span>\u6b20\u640d\u5024\u306e\u6271\u3044(ignore_na)<\/span><\/h2>\n\n\n\nignore_na\u306e\u30aa\u30d7\u30b7\u30e7\u30f3\u3092\u8a2d\u5b9a\u3059\u308b\u3053\u3068\u3067\u30c7\u30fc\u30bf\u306e\u4e2d\u306b\u6b20\u640d\u5024\u304c\u542b\u307e\u308c\u3066\u3044\u305f\u5834\u5408\u306e\u51e6\u7406\u306b\u9055\u3044\u3092\u5236\u5fa1\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n
\u4ee5\u4e0b\u306e\u30c7\u30fc\u30bf\u3092\u4f8b\u306b\u8aac\u660e\u3057\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n\n\n\n
a = [1, np.nan,2]\ndf = pd.DataFrame(a)\ndf.head()<\/code><\/pre><\/div>\n\n\n\n\u7d50\u679c\uff1a\n\t0\n0\t1.0\n1\tNaN\n2\t2.0<\/code><\/pre><\/div>\n\n\n\n<\/span>ignore_na=False\u3068\u3057\u305f\u5834\u5408<\/span><\/h3>\n\n\n\n\u5404\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306e\u7d76\u5bfe\u4f4d\u7f6e\u306b\u57fa\u3065\u3044\u3066\u91cd\u307f\u304c\u8a08\u7b97\u3055\u308c\u307e\u3059\u3002\u3064\u307e\u308a\u3001\u30a4\u30f3\u30c7\u30c3\u30af\u30b91\u306eNaN\u306e\u30c7\u30fc\u30bf\u306b\u306f\u95a2\u4fc2\u306a\u304f\u3001\u91cd\u307f\u8a08\u7b97\u304c\u884c\u308f\u308c\u307e\u3059\u3002\u308f\u304b\u308a\u3084\u3059\u304f\u03b1\u306e\u5024\u3092\u56fa\u5b9a\u3057\u305f\u4ee5\u4e0b\u306e\u30b3\u30fc\u30c9\u3067\u78ba\u8a8d\u3057\u3066\u307f\u307e\u3059\u3002com\u3084span\u306a\u3069\u306e\u304b\u308f\u308a\u306balpha\u30aa\u30d7\u30b7\u30e7\u30f3\u3092\u8a2d\u5b9a\u3059\u308b\u3053\u3068\u3067alpha\u3092\u76f4\u63a5\u6c7a\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n
df.ewm(alpha=0.2, adjust=False, ignore_na=False).mean()<\/code><\/pre><\/div>\n\n\n\n\u7d50\u679c\uff1a\n\t0\n0\t1.000000\n1\t1.000000\n2\t1.238095<\/code><\/pre><\/div>\n\n\n\n\u8a08\u7b97\u5f0f\u3092\u8003\u3048\u3066\u307f\u308b\u3068\u3001\u30a4\u30f3\u30c7\u30c3\u30af\u30b90\u306b\u3064\u3044\u3066\u306f\u3082\u3068\u3082\u3068\u306e\u5165\u529b\\(x_0\\)\u3092\u305d\u306e\u307e\u307e\u8fd4\u3057\u3001\u30c7\u30fc\u30bf\u306e\u5b58\u5728\u3057\u306a\u3044\u30a4\u30f3\u30c7\u30c3\u30af\u30b91\u306b\u3064\u3044\u3066\u306f\u3001\u73fe\u5728\u306e\u5024\u304c\u306a\u3044\u306e\u3067\u3001\u524d\u306e\u7d50\u679c\u3092\u51fa\u529b\u3057\u307e\u3059\u3002<\/p>\n\n\n\n
\\(y_0 = x_0 = 1 \\)<\/p>\n\n\n\n
\\(y_1 = y_1 \\)<\/p>\n\n\n\n
\u91cd\u8981\u306a\u306e\u306f\u30a4\u30f3\u30c7\u30c3\u30af\u30b92\u306e\u8a08\u7b97\u306b\u306a\u308a\u307e\u3059\u3002\u307e\u305a\u3001adjust=False\u306e\u901a\u5e38\u306e\u5f0f\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002 <\/p>\n\n\n\n
\\(y_2 = (1-\\alpha)^2 x_0 +\\alpha(1-\\alpha)x_1 +\\alpha \\times x_2 \\)<\/p>\n\n\n\n
\u3053\u306e\u6642\u3001\\(x_1\\)\u3067\u3042\u308b\u305f\u3081\u3001\u4f7f\u7528\u3059\u308b\u91cd\u307f\u306f \\((1-\\alpha)^2\u3068 \\alpha \\)\u3068\u3059\u308b\u306e\u304c\u3001ignore_na=False\u306e\u30aa\u30d7\u30b7\u30e7\u30f3\u3067\u3059\u3002<\/p>\n\n\n\n
\u305f\u3060\u3057\u3001\u5168\u4f53\u3067100%\u306b\u306a\u308b\u3088\u3046\u306b\u91cd\u307f\u3065\u3051\u3092\u3059\u308b\u5fc5\u8981\u304c\u3042\u308b\u305f\u3081\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u5f0f\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n
\\(y_2 = \\frac{(1-\\alpha)^2}{(1-\\alpha)^2+\\alpha} x_0 + \\frac{\\alpha}{(1-\\alpha)^2+\\alpha} x_2 \\)<\/p>\n\n\n\n
\u305d\u306e\u305f\u3081\u3001\u4eca\u56de\u306e\u4f8b\u3067\u306f\u6b21\u306e\u3088\u3046\u306b\u30a4\u30f3\u30c7\u30c3\u30af\u30b92\u306e\u7d50\u679c\u304c\u8a08\u7b97\u3055\u308c\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n
\\(y_2 = \\frac{(1-0.2)^2}{(1-0.2)^2+0.2} \\times 1 + \\frac{0.2}{(1-0.2)^2+0.2} \\times 2 = \\frac{0.64}{0.84} + \\frac{0.4}{0.84}=1.238095 \\)<\/p>\n\n\n\n
<\/span>ignore_na=True\u3068\u3057\u305f\u5834\u5408<\/span><\/h3>\n\n\n\n\u3053\u306e\u5834\u5408\u306b\u306fNaN\u3092\u7121\u8996\u3057\u3066\u76f8\u5bfe\u4f4d\u7f6e\u3067\u91cd\u307f\u8a08\u7b97\u304c\u884c\u308f\u308c\u308b\u305f\u3081\u3001\\(y_2\\)\u306e\u8a08\u7b97\u5f0f\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n
\\(y_2 = (1-\\alpha) x_0 + \\alpha x_2 = 0.8 \\times 1 +0.2 \\times 2 = 1.2\\)<\/p>\n\n\n\n
\u30d7\u30ed\u30b0\u30e9\u30e0\u3067\u78ba\u8a8d\u3059\u308b\u3068\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n
df.ewm(alpha=0.2, adjust=False, ignore_na=True).mean()<\/code><\/pre><\/div>\n\n\n\n\u7d50\u679c\uff1a\n\t0\n0\t1.0\n1\t1.0\n2\t1.2<\/code><\/pre><\/div>\n\n\n\n<\/p>\n\n\n\n
<\/span>\u307e\u3068\u3081<\/span><\/h2>\n\n\n\nPandas\u3067\u6307\u6570\u52a0\u91cd\u5e73\u5747\u306e\u8a08\u7b97\u3092\u884c\u3046\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002\u307e\u305f\u3001\u30aa\u30d7\u30b7\u30e7\u30f3\u3092\u8a2d\u5b9a\u3059\u308b\u3053\u3068\u3067\u3001\u91cd\u307f\u306e\u30d1\u30e9\u30e1\u30fc\u30bfalpha\u3084\u6b20\u640d\u5024\u304c\u3042\u3063\u305f\u5834\u5408\u306e\u51e6\u7406\u306a\u3069\u3082\u6307\u5b9a\u3059\u308b\u3053\u3068\u304c\u53ef\u80fd\u3067\u3059\u3002\u682a\u4fa1\u306e\u30c6\u30af\u30cb\u30ab\u30eb\u5206\u6790\u306a\u3069\u306e\u969b\u306b\u5f79\u306b\u7acb\u3061\u307e\u3059\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"
python\u306e\u30c7\u30fc\u30bf\u30d5\u30ec\u30fc\u30e0\u306b\u306f\u6307\u6570\u8377\u91cd(exponential w...<\/p>\n","protected":false},"author":1,"featured_media":1218,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_locale":"ja","_original_post":"https:\/\/obenkyolab.com\/?p=5485","footnotes":""},"categories":[7,114],"tags":[],"class_list":["post-5485","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-python","category-114","ja"],"_links":{"self":[{"href":"https:\/\/obenkyolab.com\/index.php?rest_route=\/wp\/v2\/posts\/5485","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/obenkyolab.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/obenkyolab.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/obenkyolab.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/obenkyolab.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=5485"}],"version-history":[{"count":30,"href":"https:\/\/obenkyolab.com\/index.php?rest_route=\/wp\/v2\/posts\/5485\/revisions"}],"predecessor-version":[{"id":5554,"href":"https:\/\/obenkyolab.com\/index.php?rest_route=\/wp\/v2\/posts\/5485\/revisions\/5554"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/obenkyolab.com\/index.php?rest_route=\/wp\/v2\/media\/1218"}],"wp:attachment":[{"href":"https:\/\/obenkyolab.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=5485"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/obenkyolab.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=5485"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/obenkyolab.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=5485"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}