code: def varsim(
      coefs,
      intercept,
      sig_u,
      steps=100,
      initial_values=None,
      seed=None,
      nsimulations=None,
  ):
      """
      Simulate VAR(p) process, given coefficients and assuming Gaussian noise
  
      Parameters
      ----------
      coefs : ndarray
          Coefficients for the VAR lags of endog.
      intercept : None or ndarray 1-D (neqs,) or (steps, neqs)
          This can be either the intercept for each equation or an offset.
          If None, then the VAR process has a zero intercept.
          If intercept is 1-D, then the same (endog specific) intercept is added
          to all observations.
          If intercept is 2-D, then it is treated as an offset and is added as
          an observation specific intercept to the autoregression. In this case,
          the intercept/offset should have same number of rows as steps, and the
          same number of columns as endogenous variables (neqs).
      sig_u : ndarray
          Covariance matrix of the residuals or innovations.
          If sig_u is None, then an identity matrix is used.
      steps : {None, int}
          number of observations to simulate, this includes the initial
          observations to start the autoregressive process.
          If offset is not None, then exog of the model are used if they were
          provided in the model
      initial_values : array_like, optional
          Initial values for use in the simulation. Shape should be
          (nlags, neqs) or (neqs,). Values should be ordered from less to
          most recent. Note that this values will be returned by the
          simulation as the first values of `endog_simulated` and they
          will count for the total number of steps.
      seed : {None, int}
          If seed is not None, then it will be used with for the random
          variables generated by numpy.random.
      nsimulations : {None, int}
          Number of simulations to perform. If `nsimulations` is None it will
          perform one simulation and return value will have shape (steps, neqs).
  
      Returns
      -------
      endog_simulated : nd_array
          Endog of the simulated VAR process. Shape will be (nsimulations, steps, neqs)
          or (steps, neqs) if `nsimulations` is None.
      """
      rs = np.random.RandomState(seed=seed)
      rmvnorm = rs.multivariate_normal
      p, k, k = coefs.shape
      nsimulations = int_like(
          nsimulations, "nsimulations", optional=True
      )
      if isinstance(nsimulations, int) and nsimulations <= 0:
          raise ValueError(
              "nsimulations must be a positive integer if provided"
          )
      if nsimulations is None:
          result_shape = (steps, k)
          nsimulations = 1
      else:
          result_shape = (nsimulations, steps, k)
      if sig_u is None:
          sig_u = np.eye(k)
      ugen = rmvnorm(
          np.zeros(len(sig_u)), sig_u, steps * nsimulations
      ).reshape(nsimulations, steps, k)
      result = np.zeros((nsimulations, steps, k))
      if intercept is not None:
          # intercept can be 2-D like an offset variable
          if np.ndim(intercept) > 1:
              if not len(intercept) == ugen.shape[1]:
                  raise ValueError(
                      "2-D intercept needs to have length `steps`"
                  )
          # add intercept/offset also to intial values
          result += intercept
          result[:, p:] += ugen[:, p:]
      else:
          result[:, p:] = ugen[:, p:]
  
      initial_values = array_like(
          initial_values, "initial_values", optional=True, maxdim=2
      )
      if initial_values is not None:
          if not (
              initial_values.shape == (p, k)
              or initial_values.shape == (k,)
          ):
              raise ValueError(
                  "initial_values should have shape (p, k) or (k,) where p is the number of lags and k is the number of equations."
              )
          result[:, :p] = initial_values
  
      # add in AR terms
      for t in range(p, steps):
          ygen = result[:, t]
          for j in range(p):
              ygen += np.dot(coefs[j], result[:, t - j - 1].T).T
  
      return result.reshape(result_shape)
  
file_path: statsmodels/statsmodels/tsa/vector_ar/util.py
imports: from statsmodels.compat.pandas import frequencies
  from statsmodels.compat.python import asbytes
  from statsmodels.tools.validation import array_like, int_like
  import numpy
  import pandas
  from scipy import stats, linalg
  import statsmodels.tsa.tsatools
label_desc: Use image node_id 8 for calling a global function with example usage: varsim(coefs, intercept, sig_u, steps, initial_values, seed, nsimulations) and returns: result