Dummy variables in the simple dynamic model.

Page 1 <img data-url='document/dummy-variables-in-the-simple-dynamic-model.html?page=1' data-page='1' class='cut-thumb lazyload' alt='Page 1: Dummy variables in the simple dynamic model.' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader039.cupdf.com/reader039/viewer/2022032105/56649d4c5503460f94a2a95e/html5/thumbnails/1.jpg' width='140' height='200' /> Dummy variables in the simple dynamic model

Page 2 <img data-url='document/dummy-variables-in-the-simple-dynamic-model.html?page=2' data-page='2' class='cut-thumb lazyload' alt='Page 2: Dummy variables in the simple dynamic model.' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader039.cupdf.com/reader039/viewer/2022032105/56649d4c5503460f94a2a95e/html5/thumbnails/2.jpg' width='140' height='200' /> Page 3 <img data-url='document/dummy-variables-in-the-simple-dynamic-model.html?page=3' data-page='3' class='cut-thumb lazyload' alt='Page 3: Dummy variables in the simple dynamic model.' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader039.cupdf.com/reader039/viewer/2022032105/56649d4c5503460f94a2a95e/html5/thumbnails/3.jpg' width='140' height='200' /> Page 4 <img data-url='document/dummy-variables-in-the-simple-dynamic-model.html?page=4' data-page='4' class='cut-thumb lazyload' alt='Page 4: Dummy variables in the simple dynamic model.' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader039.cupdf.com/reader039/viewer/2022032105/56649d4c5503460f94a2a95e/html5/thumbnails/4.jpg' width='140' height='200' /> Page 5 <img data-url='document/dummy-variables-in-the-simple-dynamic-model.html?page=5' data-page='5' class='cut-thumb lazyload' alt='Page 5: Dummy variables in the simple dynamic model.' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader039.cupdf.com/reader039/viewer/2022032105/56649d4c5503460f94a2a95e/html5/thumbnails/5.jpg' width='140' height='200' /> Dummy variables and the VAR

Page 6 <img data-url='document/dummy-variables-in-the-simple-dynamic-model.html?page=6' data-page='6' class='cut-thumb lazyload' alt='Page 6: Dummy variables in the simple dynamic model.' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader039.cupdf.com/reader039/viewer/2022032105/56649d4c5503460f94a2a95e/html5/thumbnails/6.jpg' width='140' height='200' /> The simplified model can be written as:

The expected value of the process and the cointegration relations becomes:

Page 7 <img data-url='document/dummy-variables-in-the-simple-dynamic-model.html?page=7' data-page='7' class='cut-thumb lazyload' alt='Page 7: Dummy variables in the simple dynamic model.' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader039.cupdf.com/reader039/viewer/2022032105/56649d4c5503460f94a2a95e/html5/thumbnails/7.jpg' width='140' height='200' /> The dynamic properties of the data can now be expressed as:

where

It is easy to see that:

Page 8 <img data-url='document/dummy-variables-in-the-simple-dynamic-model.html?page=8' data-page='8' class='cut-thumb lazyload' alt='Page 8: Dummy variables in the simple dynamic model.' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader039.cupdf.com/reader039/viewer/2022032105/56649d4c5503460f94a2a95e/html5/thumbnails/8.jpg' width='140' height='200' /> Illustration

Page 9 <img data-url='document/dummy-variables-in-the-simple-dynamic-model.html?page=9' data-page='9' class='cut-thumb lazyload' alt='Page 9: Dummy variables in the simple dynamic model.' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader039.cupdf.com/reader039/viewer/2022032105/56649d4c5503460f94a2a95e/html5/thumbnails/9.jpg' width='140' height='200' /> Page 10 <img data-url='document/dummy-variables-in-the-simple-dynamic-model.html?page=10' data-page='10' class='cut-thumb lazyload' alt='Page 10: Dummy variables in the simple dynamic model.' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader039.cupdf.com/reader039/viewer/2022032105/56649d4c5503460f94a2a95e/html5/thumbnails/10.jpg' width='140' height='200' /> Are the observed outliers additive or innovational?

Page 11 <img data-url='document/dummy-variables-in-the-simple-dynamic-model.html?page=11' data-page='11' class='cut-thumb lazyload' alt='Page 11: Dummy variables in the simple dynamic model.' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader039.cupdf.com/reader039/viewer/2022032105/56649d4c5503460f94a2a95e/html5/thumbnails/11.jpg' width='140' height='200' /> An additive outlier in real money stock

Page 12 <img data-url='document/dummy-variables-in-the-simple-dynamic-model.html?page=12' data-page='12' class='cut-thumb lazyload' alt='Page 12: Dummy variables in the simple dynamic model.' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader039.cupdf.com/reader039/viewer/2022032105/56649d4c5503460f94a2a95e/html5/thumbnails/12.jpg' width='140' height='200' /> The Danish VAR model with dummy variables

Page 13 <img data-url='document/dummy-variables-in-the-simple-dynamic-model.html?page=13' data-page='13' class='cut-thumb lazyload' alt='Page 13: Dummy variables in the simple dynamic model.' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader039.cupdf.com/reader039/viewer/2022032105/56649d4c5503460f94a2a95e/html5/thumbnails/13.jpg' width='140' height='200' /> Page 14 <img data-url='document/dummy-variables-in-the-simple-dynamic-model.html?page=14' data-page='14' class='cut-thumb lazyload' alt='Page 14: Dummy variables in the simple dynamic model.' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader039.cupdf.com/reader039/viewer/2022032105/56649d4c5503460f94a2a95e/html5/thumbnails/14.jpg' width='140' height='200' /> The unrestricted VAR with dummies

Page 15 <img data-url='document/dummy-variables-in-the-simple-dynamic-model.html?page=15' data-page='15' class='cut-thumb lazyload' alt='Page 15: Dummy variables in the simple dynamic model.' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader039.cupdf.com/reader039/viewer/2022032105/56649d4c5503460f94a2a95e/html5/thumbnails/15.jpg' width='140' height='200' /> We need to distinguish between:

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Dummy variables in the simple dynamic model.

Documents

var slide

illustration slide

simple dynamic model

real money stock slide

dummy variables

danish var model

unrestricted var

simplified model