Econ226_VI

Econ226_VI - 1 VI Spatiotemporal models A Introduction 2 s location s 1 2 N t date t 1 2 T y t s variable of interest Example 1(economics s 1

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Unformatted text preview: 1 VI. Spatiotemporal models A. Introduction 2 s location s 1, 2, . . . , N t date t 1, 2, . . . , T y t s variable of interest Example 1 (economics): s 1 · Alabama s N · Wyoming t 1 « 1954:I t T · 2004:IV y t s unemployment rate in Colorado in 1972:II Example 2 (Wikle, Berliner, and Cressie): s particular location in U.S. midwest at which either temperatures were recorded or are wanted to be inferred y t s average daily maximum temperature at location s in month t 3 y t y t 1 y t 2 B y t N unemployment rates for all states observed in quarter t VI. Spatiotemporal models A. Introduction B. Modeling spatial correlation time series: when something is observed at one date, it changes what we expect to see at other dates spatial data: when something is observed at one location, it changes what we expect to see at other locations 4 time series white noise: / t L N 0, @ / 2 / t independent of / A whenever t p A time series moving average: u t / t 2 / t " 1 ´ u t is correlated with u t " 1 but not with u t " 2 , u t " 3 , . . . time series autoregression: u t C u t " 1 / t ´ u t is correlated with u t " 1 , u t " 2 , . . . 5 spatiotemporal white noise: / t s L N 0, @ / 2 / t s independent of / A r whenever t p A or r p s spatial moving average: Let R s set of all states adjacent to s (note s R s ) n s number of states adjacent to s u t s 2 ¡ n s ¢ " 1 ! r R s / t r / t s u t s is independent of u t r whenever r and s are more than two states apart Let row s , column r element of B be 1/ n s if r R s and zero otherwise u t I N 2 B / t u t L N , @ 2 I N 2 B I N 2 B U 6 spatial autoregression: u t s C ¡ n s ¢ " 1 ! r R s u t r / t s u t C Bu t / t u t L N , @ / 2 I N " C B " 1 I N " C B U " 1 u t s is correlated with u t r for all r , s suppose there is a shock a t L N 0, @ a 2 that affects all states equally in addition to...
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This note was uploaded on 03/02/2012 for the course ECON 226 taught by Professor Jameshamilton during the Winter '09 term at UCSD.

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Econ226_VI - 1 VI Spatiotemporal models A Introduction 2 s location s 1 2 N t date t 1 2 T y t s variable of interest Example 1(economics s 1

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