$\mathrm{with}\left(\mathrm{Statistics}\right)\:$

$U≔\mathrm{Sample}\left(\mathrm{Normal}\left(0\,0.3\right)\,100\right)$

$U≔\left[\begin{array}{cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc}\mathrm{-0.321727238399481}& \mathrm{-0.0987233611641195}& \mathrm{-0.185127581072937}& 0.0643400235735872& \mathrm{-0.00762843841271539}& 0.518646385253350& \mathrm{-0.490457026303171}& 0.471351651526290& 0.0511075264231225& 0.301943522625543& 0.0806138037474931& \mathrm{-0.439794134087633}& \mathrm{-0.0107273561518490}& \mathrm{-0.00195100903879099}& \mathrm{-0.0171549006699714}& \mathrm{-0.0553800283874787}& 0.0611566207113337& \mathrm{-0.0296615472081370}& \mathrm{-0.0248094291125946}& \mathrm{-0.0504357384364224}& 0.0486063899603798& \mathrm{-0.202775612901785}& \mathrm{-0.132239293214560}& 0.268805995577865& 0.138306886014007& 0.383393115682154& 0.0703697885383742& \mathrm{-0.0108823473881049}& \mathrm{-0.134654437053644}& \mathrm{-0.350211925597414}& \mathrm{-0.365382865182373}& \mathrm{-0.346407588277875}& 0.0328977969850794& \mathrm{-0.185942814192385}& 0.192645301393477& \mathrm{-0.0512312754294732}& \mathrm{-0.246015672308395}& 0.403900558989702& \mathrm{-0.295811568047437}& \mathrm{-0.289751638049954}& \mathrm{-0.409387715941723}& 0.495023615869223& 0.404412454056052& \mathrm{-0.307612177855977}& 0.0689364182591729& 0.445480373904158& \mathrm{-0.390092716234762}& \mathrm{-0.112839334870862}& 0.0185352590001619& 0.240572348742312& \mathrm{-0.0389926411652577}& 0.0337453591812398& 0.189108177538398& \mathrm{-0.00626878190525176}& \mathrm{-0.249132846899220}& \mathrm{-0.0787957530423553}& \mathrm{-0.210090078590402}& 0.586670717583819& \mathrm{-0.0778422496867822}& \mathrm{-0.0246255187687290}& 0.364673835787499& \mathrm{-0.294939544127897}& 0.579207194666806& 0.0368205325760259& 0.129883626345462& \mathrm{-0.157333145358841}& 0.0672646655783495& \mathrm{-0.124267670429512}& 0.0106578408688916& 0.595113629303997& 0.664013876817107& 0.264368966588063& 0.266056935168126& \mathrm{-0.258499784192641}& \mathrm{-0.271983391002268}& \mathrm{-0.263019295304916}& \mathrm{-0.0652471378859968}& \mathrm{-0.100846552286741}& 0.164812972805739& \mathrm{-0.359264530214500}& \mathrm{-0.278253101861857}& \mathrm{-0.398985181626683}& \mathrm{-0.339130809440933}& 0.381561075201006& \mathrm{-0.442954639034717}& 0.484014747280828& \mathrm{-0.205602620810246}& 0.324723870276193& \mathrm{-0.233020470143960}& \mathrm{-0.166644431428393}& 0.321717554330475& 0.0214058932888665& \mathrm{-0.0546368773468666}& 0.188564863085573& \mathrm{-0.217755193503086}& \mathrm{-0.124014101580007}& 0.462724590346982& \mathrm{-0.0660928282271428}& \mathrm{-0.252244807425815}& 0.115519803619994\end{array}\right]$

$V≔⟨\mathrm{seq}\left(\sin \left(\frac{\mathrm{\pi }i}{10}\right)+U\left[i\right]\,i=1..100\right)⟩\:$

$P≔\mathrm{PointPlot}\left(V\right)\:$

$Q≔\mathrm{plot}\left(\sin \left(\frac{\mathrm{\pi }x}{10}\right)\,x=0..100\,\mathrm{thickness}=3\right)\:$

$\mathrm{plots}\left[\mathrm{display}\right]\left(P\,Q\right)$

$W≔\mathrm{MovingAverage}\left(V\,5\right)$

$W≔\begin{array}{c}\left[\begin{array}{c}0.621601832372371\\ 0.918084461486979\\ 0.883984076875663\\ 0.971033574979014\\ 0.839979171164879\\ 0.701893563372531\\ 0.362272344937339\\ 0.0930444740469630\\ \mathrm{-0.282731776822149}\\ \mathrm{-0.545358186048552}\\ ⋮\end{array}\right]\\ \hfill \text{96 element Vector[column]}\end{array}$

$R≔\mathrm{LineChart}\left(W\,\mathrm{xcoords}=\left[\mathrm{seq}\left(i\,i=2..98\right)\right]\,\mathrm{thickness}=3\right)\:$

$\mathrm{plots}\left[\mathrm{display}\right]\left(P\,Q\,R\right)$

$\mathrm{U1}≔\mathrm{ExponentialSmoothing}\left(V\,0.2\right)$

$\mathrm{U1}≔\begin{array}{c}\left[\begin{array}{c}\mathrm{-0.0127102440044911}\\ 0.0876441830220778\\ 0.194893229078064\\ 0.358993891236200\\ 0.485669425306417\\ 0.682476120554834\\ 0.609692890058222\\ 0.699581692810331\\ 0.631690258407878\\ 0.565740911251411\\ ⋮\end{array}\right]\\ \hfill \text{100 element Vector[column]}\end{array}$

$\mathrm{U2}≔\mathrm{ExponentialSmoothing}\left(V\,0.8\right)$

$\mathrm{U2}≔\begin{array}{c}\left[\begin{array}{c}\mathrm{-0.0127102440195227}\\ 0.388707464098778\\ 0.576853023461364\\ 0.927687836587266\\ 0.979434816587281\\ 1.37164928455626\\ 0.529177831368673\\ 0.953145089328745\\ 0.478728634504205\\ 0.337300545001275\\ ⋮\end{array}\right]\\ \hfill \text{100 element Vector[column]}\end{array}$

$R≔\mathrm{LineChart}\left(\left[\mathrm{U1}\,\mathrm{U2}\right]\,\mathrm{color}=\left[\mathrm{red}\,\mathrm{blue}\right]\,\mathrm{thickness}=3\right)\:$

$\mathrm{plots}\left[\mathrm{display}\right]\left(P\,R\right)$

$X≔⟨\mathrm{seq}\left(i\,i=1..100\right)⟩\:$

$R≔\mathrm{ScatterPlot}\left(X\,V\,\mathrm{lowess}\,\mathrm{degree}=3\,\mathrm{color}=\mathrm{blue}\,\mathrm{thickness}=3\right)\:$

$\mathrm{plots}\left[\mathrm{display}\right]\left(P\,Q\,R\right)$