Is it good practice to use Linear Least-Squares with SMA?












1












$begingroup$


I have time-series (daily) data and I want to understand the general trend.



My current approach is:




  1. Calculate the 7-day simple moving average.


  2. Add a line of best fit (linear least squares regression).


  3. Plot, then review metrics such as r, r^2, etc.



Question: is it good practice to draw a line-of-best fit on a moving average? I'm not very experienced but my understanding is MA and linear trend lines are both trend lines, so I'm not sure if it's OK to combine them in this way.



Raw data looks like this:



day             + count

2015-01-01 | 123

2015-01-02 | 290

2015-01-03 | 329

2015-01-04 | 276



Let me know if more detail would help- any direction on this is much appreciated.






regression time-series correlation trend moving-average







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  • 1




    $begingroup$
    It depends on how you compute step (2), "a line of best fit (linear least squares regression)." If you just drop the data into a least squares black box, most likely it operates under the assumption the errors are independent, whereas in a moving average the errors are strongly interdependent (e.g., neighboring 7-day averages have six days of data in common). You need to use a procedure that accounts for this. There are robust ways to explore trends, such as various nonparametric smoothers, so maybe it would be more fruitful to investigate them rather than fixing your current approach.
    $endgroup$
    – whuber♦
    3 hours ago


















1












$begingroup$


I have time-series (daily) data and I want to understand the general trend.



My current approach is:




  1. Calculate the 7-day simple moving average.


  2. Add a line of best fit (linear least squares regression).


  3. Plot, then review metrics such as r, r^2, etc.



Question: is it good practice to draw a line-of-best fit on a moving average? I'm not very experienced but my understanding is MA and linear trend lines are both trend lines, so I'm not sure if it's OK to combine them in this way.



Raw data looks like this:



day             + count

2015-01-01 | 123

2015-01-02 | 290

2015-01-03 | 329

2015-01-04 | 276



Let me know if more detail would help- any direction on this is much appreciated.






regression time-series correlation trend moving-average







share|cite|improve this question







New contributor




Chef36 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.







$endgroup$








  • 1




    $begingroup$
    It depends on how you compute step (2), "a line of best fit (linear least squares regression)." If you just drop the data into a least squares black box, most likely it operates under the assumption the errors are independent, whereas in a moving average the errors are strongly interdependent (e.g., neighboring 7-day averages have six days of data in common). You need to use a procedure that accounts for this. There are robust ways to explore trends, such as various nonparametric smoothers, so maybe it would be more fruitful to investigate them rather than fixing your current approach.
    $endgroup$
    – whuber♦
    3 hours ago
















1












1








1





$begingroup$


I have time-series (daily) data and I want to understand the general trend.



My current approach is:




  1. Calculate the 7-day simple moving average.


  2. Add a line of best fit (linear least squares regression).


  3. Plot, then review metrics such as r, r^2, etc.



Question: is it good practice to draw a line-of-best fit on a moving average? I'm not very experienced but my understanding is MA and linear trend lines are both trend lines, so I'm not sure if it's OK to combine them in this way.



Raw data looks like this:



day             + count

2015-01-01 | 123

2015-01-02 | 290

2015-01-03 | 329

2015-01-04 | 276



Let me know if more detail would help- any direction on this is much appreciated.






regression time-series correlation trend moving-average







share|cite|improve this question







New contributor




Chef36 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.







$endgroup$




I have time-series (daily) data and I want to understand the general trend.



My current approach is:




  1. Calculate the 7-day simple moving average.


  2. Add a line of best fit (linear least squares regression).


  3. Plot, then review metrics such as r, r^2, etc.



Question: is it good practice to draw a line-of-best fit on a moving average? I'm not very experienced but my understanding is MA and linear trend lines are both trend lines, so I'm not sure if it's OK to combine them in this way.



Raw data looks like this:



day             + count

2015-01-01 | 123

2015-01-02 | 290

2015-01-03 | 329

2015-01-04 | 276



Let me know if more detail would help- any direction on this is much appreciated.






regression time-series correlation trend moving-average




regression time-series correlation trend moving-average






share|cite|improve this question







New contributor




Chef36 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











share|cite|improve this question







New contributor




Chef36 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









share|cite|improve this question




share|cite|improve this question






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Chef36 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









asked 3 hours ago









Chef36Chef36

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New contributor




Chef36 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.





New contributor





Chef36 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.






Chef36 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.








  • 1




    $begingroup$
    It depends on how you compute step (2), "a line of best fit (linear least squares regression)." If you just drop the data into a least squares black box, most likely it operates under the assumption the errors are independent, whereas in a moving average the errors are strongly interdependent (e.g., neighboring 7-day averages have six days of data in common). You need to use a procedure that accounts for this. There are robust ways to explore trends, such as various nonparametric smoothers, so maybe it would be more fruitful to investigate them rather than fixing your current approach.
    $endgroup$
    – whuber♦
    3 hours ago
















  • 1




    $begingroup$
    It depends on how you compute step (2), "a line of best fit (linear least squares regression)." If you just drop the data into a least squares black box, most likely it operates under the assumption the errors are independent, whereas in a moving average the errors are strongly interdependent (e.g., neighboring 7-day averages have six days of data in common). You need to use a procedure that accounts for this. There are robust ways to explore trends, such as various nonparametric smoothers, so maybe it would be more fruitful to investigate them rather than fixing your current approach.
    $endgroup$
    – whuber♦
    3 hours ago










1




1




$begingroup$
It depends on how you compute step (2), "a line of best fit (linear least squares regression)." If you just drop the data into a least squares black box, most likely it operates under the assumption the errors are independent, whereas in a moving average the errors are strongly interdependent (e.g., neighboring 7-day averages have six days of data in common). You need to use a procedure that accounts for this. There are robust ways to explore trends, such as various nonparametric smoothers, so maybe it would be more fruitful to investigate them rather than fixing your current approach.
$endgroup$
– whuber♦
3 hours ago






$begingroup$
It depends on how you compute step (2), "a line of best fit (linear least squares regression)." If you just drop the data into a least squares black box, most likely it operates under the assumption the errors are independent, whereas in a moving average the errors are strongly interdependent (e.g., neighboring 7-day averages have six days of data in common). You need to use a procedure that accounts for this. There are robust ways to explore trends, such as various nonparametric smoothers, so maybe it would be more fruitful to investigate them rather than fixing your current approach.
$endgroup$
– whuber♦
3 hours ago












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$begingroup$

Of course you can do a fit on a moving average. That is your right. But the statistical diagnostics are not reliable anymore. The reason is that the IID property required in standard OLS are violated when you apply plain regression on a quantity that is highly autocorrelated.



Your $r^2$ will be artificially high and will insinuate a false sense of statistical significance. Think about this case, instead of a moving average do a linear fit on your original data in time first. And then do it a gain, you will get 100% $r^2$.



These models are not reliable ex-ante predictors and will have very low out-of-sample qualities.






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    $begingroup$

    Of course you can do a fit on a moving average. That is your right. But the statistical diagnostics are not reliable anymore. The reason is that the IID property required in standard OLS are violated when you apply plain regression on a quantity that is highly autocorrelated.



    Your $r^2$ will be artificially high and will insinuate a false sense of statistical significance. Think about this case, instead of a moving average do a linear fit on your original data in time first. And then do it a gain, you will get 100% $r^2$.



    These models are not reliable ex-ante predictors and will have very low out-of-sample qualities.






    share|cite|improve this answer









    $endgroup$


















      2












      $begingroup$

      Of course you can do a fit on a moving average. That is your right. But the statistical diagnostics are not reliable anymore. The reason is that the IID property required in standard OLS are violated when you apply plain regression on a quantity that is highly autocorrelated.



      Your $r^2$ will be artificially high and will insinuate a false sense of statistical significance. Think about this case, instead of a moving average do a linear fit on your original data in time first. And then do it a gain, you will get 100% $r^2$.



      These models are not reliable ex-ante predictors and will have very low out-of-sample qualities.






      share|cite|improve this answer









      $endgroup$
















        2












        2








        2





        $begingroup$

        Of course you can do a fit on a moving average. That is your right. But the statistical diagnostics are not reliable anymore. The reason is that the IID property required in standard OLS are violated when you apply plain regression on a quantity that is highly autocorrelated.



        Your $r^2$ will be artificially high and will insinuate a false sense of statistical significance. Think about this case, instead of a moving average do a linear fit on your original data in time first. And then do it a gain, you will get 100% $r^2$.



        These models are not reliable ex-ante predictors and will have very low out-of-sample qualities.






        share|cite|improve this answer









        $endgroup$



        Of course you can do a fit on a moving average. That is your right. But the statistical diagnostics are not reliable anymore. The reason is that the IID property required in standard OLS are violated when you apply plain regression on a quantity that is highly autocorrelated.



        Your $r^2$ will be artificially high and will insinuate a false sense of statistical significance. Think about this case, instead of a moving average do a linear fit on your original data in time first. And then do it a gain, you will get 100% $r^2$.



        These models are not reliable ex-ante predictors and will have very low out-of-sample qualities.







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered 3 hours ago









        Gkhan CebsGkhan Cebs

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