Forecast error

The forecast error is the difference between the observed value and its forecast based on all previous observations. If the error is denoted as ${\displaystyle e(t)}$ then the forecast error can be written as;

${\displaystyle e(t)=y(t)-{\hat {y}}(t|t-1)}$

where,

${\displaystyle y(t)}$ = observation

${\displaystyle {\hat {y}}(t|t-1)}$ = denote the forecast of ${\displaystyle y(t)}$ based on all previous observations

Forecast errors can be evaluated using a variety of methods namely mean percentage error, root mean squared error, mean absolute percentage error, mean squared error. Other methods include tracking signal and forecast bias.

For forecast errors on training data

${\displaystyle y(t)}$ denotes the observation and ${\displaystyle {\hat {y}}(t|t-1)}$ is the forecast

For forecast errors on test data

${\displaystyle y(t+h)}$ denotes the actual value of the h-step observation and the forecast is denoted as ${\displaystyle {\hat {y}}(t+h|t)}$

Dreman and Berry in 1995 "Financial Analysts Journal", argued that securities analysts' forecasts are too optimistic, and that the investment community relies too heavily on their forecasts. However, this was countered by Lawrence D. Brown in 1996 and then again in 1997 who argued that the analysts are generally more accurate than those of "naive or sophisticated time-series models" nor have the errors been increasing over time.[4][5]

Hiromichi Tamura in 2002 argued that herd-to-consensus analysts not only submit their earnings estimates that end up being close to the consensus but that their personalities strongly affect these estimates.[6]

Michael Fish - A few hours before the Great Storm of 1987 broke, on 15 October 1987, he said during a forecast: "Earlier on today, apparently, a woman rang the BBC and said she heard there was a hurricane on the way. Well, if you're watching, don't worry, there isn't!". The storm was the worst to hit South East England for three centuries, causing record damage and killing 19 people.[7]

Great Recession - The financial and economic crisis that erupted in 2007—arguably the worst since the Great Depression of the 1930s—was not foreseen by most of the forecasters, even if a few lone analysts had been predicting it for some time (for example, Nouriel Roubini and Robert Shiller). The failure to forecast the "Great Recession" has caused a lot of soul searching in the profession. The UK's Queen Elizabeth herself asked why had nobody noticed that the credit crunch was on its way, and a group of economists—experts from business, the City, its regulators, academia, and government—tried to explain in a letter.[8]

It was not just forecasting the Great Recession, but also its impact where it was clear that economists struggled. For example, in Singapore, Citi argued the country would experience "the most severe recession in Singapore’s history". The economy grew in 2009 by 3.1% and in 2010, the nation saw a 15.2% growth rate.[9][10]

At the end of 2019 the International Monetary Fund estimated global growth in 2020 to reach 3.4%, but as a result of the coronavirus pandemic, the IMF have revised its estimate in November 2020 to expect the global economy to shrink by 4.4%.[11][12]

• Calculating demand forecast accuracy
• Errors and residuals in statistics
• Forecasting
• Forecasting accuracy
• Mean squared prediction error
• Optimism bias
• Reference class forecasting