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2e:{"id":"d6606f415341288a","slug":"tvsar-spectral-usip","title":"Time-varying spectral density for US industrial production","thumbnail":"01907262053424e9f6b3ad556d07925449c6319623ed2cc184610d87d9b74c99","access_level":"public","create_time":"$D2024-08-19T17:57:36.333Z","update_time":"$D2025-02-20T13:51:34.521Z","view_time":null,"first_public_time":"$D2024-08-19T20:13:22.294Z","fork":false,"stars":0,"starred":false,"owner":{"type":"team","id":"7592a7ab121f74a0","login":"mattiasvillani","name":"Mattias Villani","avatar_url":"https://avatars-next.observableusercontent.com/a440aaf39a3abefb86cbcc758fd7a5ab42555ae68d6825b52ec006f385a94d1d","tier":"pro_2024"},"version":374,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"56499be8cf43f0ef","login":"mattiasvillani","name":"Mattias Villani","avatar_url":"https://avatars-next.observableusercontent.com/a440aaf39a3abefb86cbcc758fd7a5ab42555ae68d6825b52ec006f385a94d1d","tier":null}],"members":[{"type":"individual","id":"56499be8cf43f0ef","login":"mattiasvillani","name":"Mattias Villani","avatar_url":"https://avatars-next.observableusercontent.com/a440aaf39a3abefb86cbcc758fd7a5ab42555ae68d6825b52ec006f385a94d1d","tier":null,"role":"editor"},{"type":"team","id":"7592a7ab121f74a0","login":"mattiasvillani","name":"Mattias Villani","avatar_url":"https://avatars-next.observableusercontent.com/a440aaf39a3abefb86cbcc758fd7a5ab42555ae68d6825b52ec006f385a94d1d","tier":"pro_2024","role":"viewer"}],"comments":[],"custom_thumbnail":false,"trashed":false,"subscribed":null,"forks":0,"collection":{"id":"3016e10448215bcd","slug":"research","title":"Research","owner":{"id":"7592a7ab121f74a0","login":"mattiasvillani","name":"Mattias Villani"}},"type":"notebook","body":{"title":"Time-varying spectral density for US industrial production","cells":[{"id":0,"value":"# Time-varying spectral density for US industrial production","pinned":false,"hidden":false,"mode":"md"},{"id":368,"value":"> Illustration of the (instantaneous) time-varying spectral density for US industrial production from the paper:
\n> Fagerberg, G., Villani,M. and Kohn, R. (2024). Time-Varying Multi-Seasonal AR Models, [arXiv](https://arxiv.org/abs/2409.18640).","pinned":false,"hidden":false,"mode":"md"},{"id":224,"value":"viewof date = Inputs.form({\n year: Inputs.range([1922, 2024], {value: 1922, label: \"year\", step: 1}),\n month: Inputs.range([1, 12], {value: 1, label: \"month\", step: 1})\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":284,"value":"viewof plotselector = Inputs.checkbox([\"95 % intervals\", \"static model\"], {label: \"plot:\", value: [\"95 % intervals\"]})","pinned":false,"hidden":false,"mode":"ojs"},{"id":319,"value":"viewof plotlog = Inputs.toggle({label: \"plot log f(ω)\", value: true})","pinned":false,"hidden":false,"mode":"ojs"},{"id":29,"value":"specplot = Plot.plot({\n y: {\n //label: \"log Spectral density log f(ω)\",\n label: yaxislabel,\n transform: (x) => {if (!plotlog){return Math.exp(x)}else{return x}},\n domain: plotlog? ylims: ylims.map(d => Math.exp(d))\n },\n x: {label: \"Angular frequency ω\"},\n title: title,\n marks: [\n Plot.ruleY([-15]),\n Plot.ruleX([0]),\n Plot.areaY(specdensdata, {filter: plotselector.includes(\"95 % intervals\"), x: \"ω\", y1: \"low\", y2: \"high\", fill: \"#F0F0F0\"}),\n Plot.lineY(specdensdata, {filter: plotselector.includes(\"95 % intervals\"), x: \"ω\", y: \"low\", stroke: \"gray\", strokeWidth: 1}),\n Plot.lineY(specdensdata, {filter: plotselector.includes(\"static model\"), x: \"ω\", y: \"static\", stroke: colors[1], strokeWidth: 2}),\n Plot.lineY(specdensdata, {x: \"ω\", y: \"med\", stroke: colors[2], strokeWidth: 2}),\n Plot.lineY(specdensdata, {filter: plotselector.includes(\"95 % intervals\"), x: \"ω\", y: \"high\", stroke: \"gray\", strokeWidth: 1})\n ]\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":58,"value":"
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\n\n---\n## 🙈 Appendix 🙈\nHere follow code and details that you probably do not want to read.","pinned":false,"hidden":false,"mode":"md"},{"id":81,"value":"#### Imports","pinned":false,"hidden":false,"mode":"md"},{"id":83,"value":"import {colors} from \"@mattiasvillani/statistics-tools\"","pinned":false,"hidden":false,"mode":"ojs"},{"id":99,"value":"#### Functions","pinned":false,"hidden":false,"mode":"md"},{"id":267,"value":"function getMonthName(monthNumber) {\n const months = [\n \"Jan\", \"Feb\", \"Mar\", \"Apr\", \"May\", \"Jun\",\n \"Jul\", \"Aug\", \"Sep\", \"Oct\", \"Nov\", \"Dec\"\n ];\n\n // Check if monthNumber is within valid range\n if (monthNumber >= 1 && monthNumber <= 12) {\n return months[monthNumber - 1]; // Adjust index (months array is zero-indexed)\n } else {\n return \"Invalid month number\"; // Handle invalid input gracefully\n }\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":236,"value":"function timeFromYearMonth(year, month, startyear, startmonth){\n return 1 + (month - startmonth) + (year-startyear)*12 \n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":60,"value":"#### Data","pinned":false,"hidden":false,"mode":"md"},{"id":270,"value":"t = timeFromYearMonth(date.year, date.month, 1921, 2) - 1","pinned":false,"hidden":false,"mode":"ojs"},{"id":62,"value":"low = FileAttachment(\"usipSAR12_param_spec_low@1.csv\").csv({array: true, typed: true})","pinned":false,"hidden":false,"mode":"ojs"},{"id":64,"value":"med = FileAttachment(\"usipSAR12_param_spec_med@1.csv\").csv({array: true, typed: true})","pinned":false,"hidden":false,"mode":"ojs"},{"id":66,"value":"high = FileAttachment(\"usipSAR12_param_spec_high@1.csv\").csv({array: true, typed: true})","pinned":false,"hidden":false,"mode":"ojs"},{"id":295,"value":"medstatic = FileAttachment(\"usipSAR12_param_spec_static.csv\").csv({array: true, typed: true})","pinned":false,"hidden":false,"mode":"ojs"},{"id":50,"value":"ωgrid = d3.range(0.01, Math.PI, 0.01)","pinned":false,"hidden":false,"mode":"ojs"},{"id":25,"value":"specdensdata = {\n var data = [];\n var lowsnap = low[t]\n for (let index = 0; index < ωgrid.length; ++index) {\n data.push({ω: ωgrid[index], low: low[t][index], med: med[t][index], high: high[t][index], static: medstatic[t][index]})\n }\n return data\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":35,"value":"title = { \n if (date.year >= 1929 && date.year <= 1939){\n return md`${getMonthName(date.month)}, ${date.year} 😔`\n }\n if(date.year >= 2020 && date.year <= 2022){\n return md`${getMonthName(date.month)}, ${date.year} 😷`\n }else{\n return md`${getMonthName(date.month)}, ${date.year}`\n }\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":324,"value":"yaxislabel = {if (plotlog){return \"log Spectral density log f(ω)\"}else{return \"Spectral density f(ω)\"}}","pinned":false,"hidden":false,"mode":"ojs"},{"id":330,"value":"ylims = {\n if (plotselector.includes(\"95 % intervals\")){\n return d3.extent(specdensdata.map(d => d.low).concat(specdensdata.map(d => d.high)))\n }else{\n return d3.extent(specdensdata.map(d => d.med).concat(specdensdata.map(d => d.static)))\n }\n}","pinned":true,"hidden":false,"mode":"ojs"}],"files":"$W31","stdlib":"1","titling":"auto"}} 2f:"$2e:body"