So, for instance, we can have a dependent variable that is quarterly, and a regressor that is measured at a monthly, or daily, frequency… a MIDAS regression model is a very general type of autoregressive-distributed lag model, in which high-frequency data are used to help in the prediction of a low-frequency variable…Typically, some ‘extra’ values the high-frequency variable(s) will be available after the most recent sample value of the low-frequency dependent variable has been observed…These ‘extra’ observations can be used for…nowcasting.”
“A MIDAS regression model allows us to ‘explain’ a time-series variable that’s measured at some frequency, as a function of current and lagged values of a variable that is measured at a higher frequency. When the difference in sampling frequencies between the regressand and the regressors is large, distributed lag functions are typically employed to model dynamics avoiding parameter proliferation.” “Mixed-data sampling (MIDAS) regressions allow estimating dynamic equations that explain a low-frequency variable by high-frequency variables and their lags.
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The challenge is how to best use available data.” Most financial variables (e.g., interest rates and asset prices), on the other hand, are sampled daily or even more frequently. Most macroeconomic data are sampled monthly (e.g., employment) or quarterly (e.g., GDP). “Data are not all sampled at the same frequency.
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“Mixed data sampling (MIDAS) regressions are now commonly used to deal with time series data sampled at different frequencies.” The post ties up with this site’s summary on quantititative methods for macro information efficiency. Cursive text and text in brackets have been added for clarity. The below are condensed annotated quotes. The sources of the post are summarized at the bottom. In practice, MIDAS has been used for nowcasting financial market volatility, GDP growth, inflation trends and fiscal trends. The R package ‘midasr’ estimates models for multiple frequencies and weighting schemes. Compared to state-space models ( view post here), MIDAS simplifies specification and theory-based restrictions for nowcasting. Analogously, reverse MIDAS models predict a high-frequency dependent variable based on low-frequency explanatory variables. The most common MIDAS predictions rely on distributed lags of higher frequency regressors to avoid parameter proliferation. For instance, the dependent variable could be quarterly GDP and the explanatory variables could be monthly activity or daily market data. Mixed data sampling (MIDAS) regressions explain a low-frequency variable based on high-frequency variables and their lags. Nowcasting macro-financial indicators requires combining low-frequency and high-frequency time series.