state_space_forecasts_for_sve: Forecasts for Single View Embedding Based on Only the Nearest...

In luke-a-rogers/pbsedm: An R package to implement some of the methods of empirical dynamic modelling

Forecasts for Single View Embedding Based on Only the Nearest Neighbour, Not Simplex

Description

Adapting, simplifying and correcting 'state_space_forecasts()' to be called from ‘single_view_embedding()'. Based on what’s described in Hao and Sugihara (2016; Science 353:922). This function will do some of the following steps in one go (basically looping through the t* values).

Usage

state_space_forecasts_for_sve(
  ssr_input,
  distance,
  lags_of_response_variable,
  response_s
)

Arguments

ssr_input	[matrix()] a state space reconstruction in which the rows are points in the state space
distance	[matrix()] of distances of allowed neighbours
lags_of_response_variable	NULL or vector of lags being considered for the response variable, to help eliminate invalid candidate nearest neighbours
response_s	vector of values of scaled response variable, which may or may not be in the 'ssr_input'

Details

Steps are (basically a modified version of our Table 3 in manuscript 1) TODO add to manuscript, move elsewhere - take a single view embedding (input into here), which is matrix X in manuscript 1, with each row representing time and each column a component (dimension) of the state space - pick focal time 't&*' to make projection from, we need to know 'x_t^*+1' (see allowable focal values 't^*' in manuscript 1) - define the set of candidate nearest neighbours to 'x_t^*' - find the single nearest neighbour of the focal point 'x_t^*' - make a projection of 'x_t^*+1' based on that neighbour (no weighting needed, though we could add that in if necessary) - Repeat for all appropriate focal times 't^*' - Calculate the correlation coefficient between predictions and known observations - TODO make this just based on our response variable or on all dimensions??? First seems sensible, but second seems to be capturing more of the ethos of Takens' theorem. - In Simplex the above would be repeated for different 'E', in multiview we will repeat this for different views (state space reconstructions) in 'multiview_embedding()', which will call the current function.

Return the projected values of the ssr, to then be used to calculate the correlation coefficient (or metric of interest) and make the forecast if this particular sve is deemed good.

Value

[vector()] where index of each element corresponds to a 't^*', and the value of the element gives the index of the projection (i.e. projection for 't^*+1', based on where the nearest neighbour went). Because just using the single nearest neighbour, can just return indices and deal with of indices of projections for each 't^* + 1'projected values of t, including for 'T+1'.

Author(s)

Andrew M. Edwards and Luke A. Rogers

luke-a-rogers/pbsedm documentation built on June 3, 2024, 5:20 a.m.