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The ISM Manufacturing Index is projected to post a marginal rise to 50.9 in Friday's January update, based on The Capital Spectator's average econometric forecast. That's modestly above the neutral 50 reading and roughly in line with three consensus forecasts.

Here's a closer look at the numbers, followed by brief summaries of the methodologies behind The Capital Spectator's projections:

VAR-1: A vector autoregression model that analyzes the history of industrial production in context with the ISM Manufacturing Index. The forecasts are run in R with the "vars" package.

VAR-8: A vector autoregression model that analyzes eight economic time series in context with the ISM Manufacturing Index. The eight additional series: industrial production, private non-farm payrolls, index of weekly hours worked, US stock market (S&P 500), real personal income less current transfer receipts, real personal consumption expenditures, spot oil prices, and the Treasury yield spread (10 year Note less 3-month T-bill). The forecasts are run in R with the "vars" package.

ARIMA: An autoregressive integrated moving average model that analyzes the historical record of the ISM Manufacturing Index in R via the "forecast"package.

ES: An exponential smoothing model that analyzes the historical record of the ISM Manufacturing Index in R via the "forecast" package.

Source: ISM Manufacturing Index: January 2013 Preview