# Right Way to Extrapolate Data

I have a time-series data containing 27 values (of no. of Vehicles) from 1990 to 2016. I wanted to predict - based on the underlying trend - the values upto 2050 (which is a long shot I agree).

Upon doing some research, I found that it can be done by methods like HoltWinters or TBATS which, even though, did not go with my own plan of using some Machine Learning algorithm.

I am using R for all my work. Now, after using HoltWinters() and then forecast() methods, I did get an extrapolated curve uptil 2050 but it is a simple exponential curve from 2017 to 2050 which I think I could have obtained through meager calculations.

My question is twofold:

1) What would be the best approach to obtain a meaningful extrapolation?

2) Does my current approach be modified to give me a more meaningful extrapolation?

By meaningful I want to express that a curve with the details more closer to actuality.

PS: The data that I am working with is the following:-

      Cars    Bikes  Buses Trucks
1   682600  1250700  84000 105200
2   732000  1381100  89100 107200
3   819400  1497000  95000 111400
4   868200  1573400  98700 114400
5   902700  1679300 107400 118400
6   923600  1754700 113500 119200
7   966700  1842500 114400 123700
8  1068100  1995400 119400 131300
9  1086000  2068700 125900 132900
10 1162900  2175500 150100 145100
11 1182300  2260800 154400 148600
12 1198918  2283381 161507 155793
13 1279362  2341051 155555 169274
14 1289854  2379260 165846 177478
15 1298353  2609442 166136 179727
16 1318488  2649910 168713 182516
17 1372191  2757842 175589 189950
18 1440801  2895734 184368 199447
19 1549854  3039815 187367 202574
20 1657860  3215583 195163 210944
21 1726347  4305121 198790 216119
22 1881560  5781953 202476 225075
23 2094289  7500182 215374 240888
24 2281083  9064547 220347 247197
25 2400690 10341326 223624 251339
26 2531592 12177352 228180 257483
27 2582149 12600402 228790 260422


Right now, I am working with a single column at a time (i.e. Cars) at a time for creating models and predicting.

Thanks a lot.

• sometimes "meager calculations" i.e. based upon some meager assumptions leads to the same model that a robust/rich method would obtain . If you post your 16 values I will demonstrate this. Feb 10, 2018 at 13:00
• Sure. Thanks a lot. I will add these values to my Question and they are 27 now. Feb 10, 2018 at 13:46
• One more thing @IrishStat, even if the same model is created, would it be worthy enough to use? I mean, right now, using HoltWinters and TBATS I simply obtain an Exponential Curve extrapolating after 2017 till 2050 ! Feb 10, 2018 at 13:53

## 1 Answer

If you apply the same assumed model (meagre analysis) you are imposing a specification. Time series analysis listens to the data , challenges unusual values , detects nuances and separates the observations to signal (fitted values) and noise . The signal is then extrapolated and forecast confidence limits are generated based possible reoccurring of anomalies.

Using AUTOBOX , a piece of software that I helped to develop . I obtained and and and . The equation for cars is here

• Thank you sir for going through all this effort. Really appreciate it. Feb 11, 2018 at 17:52
• If you are happy with my answer , please accept it and close the question. Feb 13, 2018 at 13:07
• Dear Sir, most regretfully, I would've accepted the answer if you would've included the address to these 2 points:- 1) What would be the best approach to obtain a meaningful extrapolation? 2) Does my current approach be modified to give me a more meaningful extrapolation? I am indeed very solemnly fond of your answer and am in fact going to use your graphs as well in my report (which I wouldn't if you have any reservations regarding). If I am mistaken please do correct me. Feb 13, 2018 at 13:21
• 1) The best approach is to form a model containing memory (arima) and any needed support variables e,g, pulses 2) your current approach is insufficient as no consideration is given to pulses as part of the equation. You are free to use any and all of my results as you see fit. Feb 13, 2018 at 13:33