33:[] 31:{"title":"Local trend model","cells":[{"id":0,"value":"# Local trend model","pinned":false,"hidden":false,"mode":"md"},{"id":194,"value":"The local trend model is\n\n${tex`\n\\begin{aligned}\n y_t &= \\mu_t + \\varepsilon_t, \\hspace{1.7cm} \\varepsilon_t \\sim N(0, \\sigma_\\varepsilon^2) \\\\\n \\mu_t &= \\mu_{t-1} + \\nu_{t-1} + \\eta_t, \\quad \\eta_t \\sim N(0, \\sigma_\\eta^2) \\\\\n \\nu_t &= \\nu_{t-1} + \\omega_t, \\hspace{1cm} \\quad \\omega_t \\sim N(0, \\sigma_\\omega^2)\n\\end{aligned}\n`}\n\n","pinned":false,"hidden":false,"mode":"md"},{"id":463,"value":"#### Settings","pinned":false,"hidden":false,"mode":"md"},{"id":162,"value":"viewof input = Inputs.form({\n n: Inputs.range([10, 1000], {value: 100, step: 1, label: \"time series length\"}),\n sigmaeps: Inputs.range([Number.EPSILON, 5], {value: 1, step: 0.1, label: tex`\\text{std error, }\\sigma_\\varepsilon`}),\n sigmaeta: Inputs.range([Number.EPSILON, 2], {value: 1, step: 0.1, label: tex`\\text{std innovation, }\\sigma_\\eta`}),\n sigmaomega: Inputs.range([Number.EPSILON, 0.5], {value: 0.01, step: 0.01, label: tex`\\text{std innovation, }\\sigma_\\omega`})\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":1118,"value":"viewof plotselector = Inputs.checkbox([\"time series, xₜ\", \"local level, μₜ\", \"local trend, νₜ\"], {label: \"plot:\", value: [\"time series, xₜ\", \"local level, μₜ\"]})","pinned":false,"hidden":false,"mode":"ojs"},{"id":781,"value":"viewof simulatebutton = Inputs.button(\"Simulate new data\")","pinned":false,"hidden":false,"mode":"ojs"},{"id":1041,"value":"timeplot = Plot.plot({\n color: {\n legend: true,\n domain: [\"time series, xₜ\", \"local level, μₜ\", \"local trend, νₜ\"],\n range: [colors[0], colors[1], colors[2]]\n },\n marks: [\n Plot.ruleX([0]),\n Plot.ruleY([d3.min(simulatedData.map(d => d.x))]),\n Plot.lineY(simulatedData, {\n filter: d => d.type == \"time series, xₜ\" && plotselector.includes(\"time series, xₜ\"), \n x: \"time\", y: \"x\", stroke: \"type\", strokeWidth: 2}),\n Plot.lineY(simulatedData, {\n filter: d => d.type == \"local level, μₜ\" && plotselector.includes(\"local level, μₜ\"), \n x: \"time\", y: \"x\", stroke: \"type\", strokeWidth: 2}),\n Plot.lineY(simulatedData, {\n filter: d => d.type == \"local trend, νₜ\" && plotselector.includes(\"local trend, νₜ\"), \n x: \"time\", y: \"x\", stroke: \"type\", strokeWidth: 2}),\n ]\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":13,"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":15,"value":"#### Imports","pinned":false,"hidden":false,"mode":"md"},{"id":11,"value":"math = require(\"mathjs\");","pinned":false,"hidden":false,"mode":"ojs"},{"id":1185,"value":"import {simLocalTrend} from \"@mattiasvillani/statistics-tools\"","pinned":false,"hidden":false,"mode":"ojs"},{"id":816,"value":"jStat = require(\"jstat\");","pinned":false,"hidden":false,"mode":"ojs"},{"id":1223,"value":"import {colors} from \"@mattiasvillani/statistics-tools\"","pinned":true,"hidden":false,"mode":"ojs"},{"id":96,"value":"#### Data","pinned":false,"hidden":false,"mode":"md"},{"id":1013,"value":"n = input.n","pinned":false,"hidden":false,"mode":"ojs"},{"id":94,"value":"#### Functions","pinned":false,"hidden":false,"mode":"md"},{"id":519,"value":"simulatedData = {\n simulatebutton\n return simLocalTrend(n, input.sigmaeps, input.sigmaeta, input.sigmaomega)\n}","pinned":false,"hidden":false,"mode":"ojs"}],"files":"$W33","stdlib":"1","titling":"auto"}