Simple Exponential Smoothing: Keep the Future Row Separate

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<body class=""><main><header><div class="eyebrow">Prepared example · source and evidence</div><h1>Simple Exponential Smoothing: Keep the Future Row Separate</h1><p>For observations 10,14,12,18 and alpha 0.5, copying the last actual gives 18. <mark>The next one-step forecast is 15</mark>. The period-four forecast stays 12 because its own observation cannot predict itself.</p></header>
<nav><button type="button" id="sample">Load sample</button><button type="button" id="add">Add row</button><button type="button" id="remove">Remove last row</button><button type="button" id="reset">Reset</button></nav><label for="alpha">Alpha (0 < alpha ≤ 1)</label><input id="alpha" type="text" value=""><div id="rows"></div><nav><button type="button" id="calculate">Calculate</button></nav><p id="result" class="result" role="status"></p><p id="roundingNote">Calculated values are displayed rounded to six decimal places; calculations retain unrounded values.</p><div id="ledger" class="ledger"></div><pre id="record" aria-label="Complete forecast calculation record"></pre>
<footer>Keep the observation order and common unit with your calculation record.</footer></main><script>
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(function(){let values=['',''];function clear(){set('result','Inputs changed; calculate again.');set('ledger','');set('record','');}function rows(){q('rows').innerHTML=values.map((v,i)=>field('y'+i,'Observation '+(i+1),v)).join('');values.forEach((_,i)=>q('y'+i).addEventListener('input',()=>{values[i]=q('y'+i).value;clear();}));clear();}on('sample',()=>{values=['10','14','12','18'];q('alpha').value='0.5';rows();});on('add',()=>{if(values.length<50){values.push('');rows();}});on('remove',()=>{if(values.length>2){values.pop();rows();}});q('alpha').addEventListener('input',clear);on('calculate',()=>{const syntax=/^\d+(?:\.\d{1,6})?$/,raw=q('alpha').value.trim(),a=Number(raw);if(!syntax.test(raw)||a<=0||a>1||values.some(v=>!syntax.test(v.trim())||Number(v)>1e6)){clear();set('result','Enter 2–50 nonnegative observations up to 1000000, and alpha greater than 0 through 1; use at most six decimal places.');return;}const ys=values.map(Number),out=[[1,ys[0],'—','—','—']];let forecast=ys[0],sse=0;for(let i=1;i<ys.length;i++){const error=ys[i]-forecast;sse+=error*error;out.push([i+1,ys[i],fmt(forecast),fmt(error),fmt(error*error)]);forecast=a*ys[i]+(1-a)*forecast;}out.push([ys.length+1,'Not observed',fmt(forecast),'—','—']);set('result',`Next forecast ${fmt(forecast)}; SSE ${fmt(sse)}; ${ys.length-1} forecastable errors; MSE ${fmt(sse/(ys.length-1))}. F2=y1; no F1.`);table('ledger',['Period','Actual','Forecast','Error','Squared error'],out);set('record','Alpha: '+a+'\nSeed: F2=y1; no F1\nCalculated values are displayed rounded to six decimal places; calculations retain unrounded values.\nPeriod,Actual,Forecast,Error,Squared error\n'+out.map(r=>r.join(',')).join('\n')+'\nForecastable error count: '+(ys.length-1)+'\nSSE: '+fmt(sse)+'\nMSE: '+fmt(sse/(ys.length-1))+'\nNext forecast (period '+(ys.length+1)+'): '+fmt(forecast));});on('reset',()=>{values=['',''];q('alpha').value='';rows();});rows();})();})();
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