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1.

linear equation

Yi,new = C 1Yi,old + C2X2,j + C3X3,k + C4X4,l + C5X5,m + C6

2.

multiplication

Yi = X1,jX{~}2,kk~

3.

division

Yi = X1,j / X2,k

4.

involution

Yi = X1,jX2,k

5.

natural logarithm

Yi = ln(Xj)

6.

common logarithm

Yi = 10 log(Xj)

7.

exponential

Yi = exp(Xj)

8.

power of 10

Yi = 10Xj

9.

power

Yi = XjC1{}

10.

power of constant

Yi = C1Xj

11.

polynomial

Yi = C0+C1X1,j + C2X1,j2 + C3X1,j3 + C4X1,j4

12.

conditional

Yi = max (X1,j, X2,k, X3,l, X4,m, C)

13.

conditional

Yi = min (X1,j, X2,k, X3,l, X4,m, C)

14.

conditional

Yi = mean (X1,j, X2,k, X3,l, X4,m )

15.

drift

Yi = X1 + C1dt + C0

16.

conditional

if Xi < C1 then Yi = C0 else Yi = Xi

17.

conditional

if Xi > C1 then Yi = C0 else Yi = Xi

18.

conditional

if Xi < C1 then Yi = C0 else Yi = Xi

19.

conditional

if Xi = missing then Yi = C0 else Yi = Xi

20.

conditional

if X1 = missing then Y = X2 2~ else Y = X1 1~

where:

Xp = equidistant time series p
Cp = coefficients

...

Non-equidistant time series can be transformed into equidistant time series. The function computes the equidistant values in 2 steps. First it aggregates the non-equidistant time steps to equidistant time steps, when calculating the function makes a difference between accumulated parameters and instantaneous parameters. Generally, the non-equidistant series may not fill all equidistant time steps. You can select one of the following options to fill in the gaps:

Section
Column
width15%
  • zero:
  • missing:
  • linear interpolation:
  • equal to last:
Column
width85%

the series values at intermediate time steps will be filled with zero's

...

the series values at intermediate time steps will be filled with missing values

...

the series values at intermediate time steps will be a linear interpolation between surrounding non-equidistant series observations

...

the series values at intermediate time steps will be equal to the last observation, (i.e. block-type filling-in).


A special option is "Average over time step". This option uses a weighted average over the values in the next time step. In the previous example, the value for 01-01-2000 05:30 is 0.0033, this is the weighted average for all time steps between 05:00 and 05:30 ((15*-0.015 + 2*0.019 + 5*0.017 + 6*0.026 + 2*0.022)/30 = 0.0033). For filling the gaps the value of the next time step is used.

Example:
The underneath table shows the differences between the 4 options for filling in the gaps.

Original Series

 

Equidistant

 

 

 

 

 

 

 

 

Zero

Missing

Linear

Equal Last

Average

01-01-2000 00:15

-0.049

01-01-2000

-0.049

-0.049

-0.049

-0.049

-0.0495

01-01-2000 00:30

-0.05

01-01-2000 00:30

-0.05

-0.05

-0.05

-0.05

-0.0500

01-01-2000 00:45

-0.05

01-01-2000 01:00

0

 

-0.045

-0.05

-0.0405

01-01-2000 01:45

-0.04

01-01-2000 01:30

-0.04

-0.04

-0.04

-0.04

-0.0405

01-01-2000 02:00

-0.041

01-01-2000 02:00

-0.041

-0.041

-0.041

-0.041

0.0033

01-01-2000 05:45

-0.015

01-01-2000 02:30

0

 

-0.03346

-0.041

0.0033

01-01-2000 05:47

0.019

01-01-2000 03:00

0

 

-0.02593

-0.041

0.0033

01-01-2000 05:52

0.017

01-01-2000 03:30

0

 

-0.01839

-0.041

0.0033

01-01-2000 05:58

0.026

01-01-2000 04:00

0

 

-0.01086

-0.041

0.0033

01-01-2000 06:00

0.022

01-01-2000 04:30

0

 

-0.00332

-0.041

0.0033

01-01-2000 06:15

0

01-01-2000 05:00

0

 

0.004214

-0.041

0.0033

01-01-2000 09:15

-0.01

01-01-2000 05:30

0.01175

0.01175

0.01175

0.01175

0.0033

01-01-2000 09:30

-0.013

01-01-2000 06:00

0.011

0.011

0.011

0.011

0.0000

01-01-2000 09:45

-0.013

01-01-2000 06:30

0

 

0.0075

0.011

-0.0115

01-01-2000 10:00

-0.014

01-01-2000 07:00

0

 

0.004

0.011

-0.0115

01-01-2000 10:15

-0.008

01-01-2000 07:30

0

 

0.0005

0.011

-0.0115

01-01-2000 10:30

-0.009

01-01-2000 08:00

0

 

-0.003

0.011

-0.0115

01-01-2000 10:45

-0.022

01-01-2000 08:30

0

 

-0.0065

0.011

-0.0115

 

 

01-01-2000 09:00

-0.01

-0.01

-0.01

-0.01

-0.0115

 

 

01-01-2000 09:30

-0.013

-0.013

-0.013

-0.013

-0.0135

 

 

01-01-2000 10:00

-0.011

-0.011

-0.011

-0.011

-0.0085

 

 

01-01-2000 10:30

-0.0155

-0.0155

-0.0155

-0.0155

-0.0220

...

Errors may have an accumulative character, when the phenomenon causing the error has to do e.g. with siltation, weed growth, etc. hymosoffers the possibility to correct for this type of error by applying a continuously growing adjustment from the time the error is thought to have commenced till the error was detected and quantified. Let the error be DX observed at time t=i+k and assumed to have commenced k intervals before, then the applied correction reads:

X corr,j = X meas,j - ((j-i)/k)DX for ΔX           for j = i, i+1, . ..., i+k

Input for this option are:

  • series code,
  • start and end date of the series correction
  • error DX ΔX (mind the sign of the correction!)

...