1. I think the author is probably talking about the residuals of the model. I argue this because of his statement about adding more fourier coefficients; if, as I believe, he is fitting a fourier model, then obviously adding more coefficients will reduce the autocorrelation of the residuals at the expense of a higher CV (because of overfitting). In this context, autocorrelation on the residuals is 'bad', because it means you are not modeling the correlation between datapoints well enough.
2. The main reason why people don't difference the series is because they actually want to model the underlying process as it is. One differences the time series usually to get rid of periodicities or trends, but if that periodicity or trend is actually what you are trying to model, then differencing them might seem like a last resort option (or an option in order to model the residuals with a more complex stochastic process).
3. This really depends on the area you are working on. It could be a problem with the deterministic model also. However, depending on the form of the autocorrelation, it can be easily seen when the autocorrelation arises due to, e.g., flicker noise, ARMA-like noise or if it is a residual underlying periodic source (in which case you would maybe want to increase the number of fourier coefficients).

1. I think the author is probably talking about the residuals of the model. I argue this because of his statement about adding more fourier coefficients; if, as I believe, he is fitting a fourier model, then adding more coefficients will reduce the autocorrelation of the residuals at the expense of a higher CV.

If you have trouble visualizing this, think of the following example: suppose you have the following 100 points data set, which comes from a two-coefficient fourier model with addeded white gaussian noise:

The following graph shows two fits: one done with 2 fourier coefficients, and one done with 200 fourier coefficients:

As you can see, the 200 fourier coefficients fits the DATAPOINTS better, while the 2 coefficient fit (the 'real' model) fits the MODEL better. This implies that the autocorrelation of the residuals of the model with 200 coefficients will almost surely be closer to zero at all lags than the residuals of the 2 coefficient model, because the model with 200 coefficients fits exactly almost all datapoints (i.e., the residuals will be almost all zeros). However, what would you think will happen if you leave, say, 10 datapoints out of the sample and fit the same models? The 2-coefficient model will predict better the datapoints you leaved out of the sample! Thus, it will produce a lower CV error as opossed to the 200-coefficient model; this is called overfitting. The reason behind this 'magic' is because what CV actually tries to measure is prediction error, i.e., how well your model predicts datapoints not in your dataset. 2. In this context, autocorrelation on the residuals is 'bad', because it means you are not modeling the correlation between datapoints well enough. The main reason why people don't difference the series is because they actually want to model the underlying process as it is. One differences the time series usually to get rid of periodicities or trends, but if that periodicity or trend is actually what you are trying to model, then differencing them might seem like a last resort option (or an option in order to model the residuals with a more complex stochastic process). 3. This really depends on the area you are working on. It could be a problem with the deterministic model also. However, depending on the form of the autocorrelation, it can be easily seen when the autocorrelation arises due to, e.g., flicker noise, ARMA-like noise or if it is a residual underlying periodic source (in which case you would maybe want to increase the number of fourier coefficients).

1. I think the author is probably talking about the residuals of the model. I argue this because of his statement about adding more fourier coefficients; if, as I believe, he is fitting a fourier model, then obviously adding more coefficients will reduce the autocorrelation of the residuals at the expense of a higher CV (because of overfitting). In this context, autocorrelation on the residuals is bad, because it means you are not modeling the correlation between datapoints well enough.
2. The main reason why people don't difference the series is because they actually want to model the underlying process as it is. One differences the time series usually to get rid of periodicities or trends, but if that periodicity or trend is actually what you are trying to model, then differencing them might seem like a last resort option.
3. This really depends on the area you are working on. It could be a problem with the deterministic model also. However, depending on the form of the autocorrelation, it can be easily seen when the autocorrelation arises due to, e.g., flicker noise, ARMA-like or if it is a residual underlying periodic source.

1. I think the author is probably talking about the residuals of the model. I argue this because of his statement about adding more fourier coefficients; if, as I believe, he is fitting a fourier model, then obviously adding more coefficients will reduce the autocorrelation of the residuals at the expense of a higher CV (because of overfitting). In this context, autocorrelation on the residuals is 'bad', because it means you are not modeling the correlation between datapoints well enough.
2. The main reason why people don't difference the series is because they actually want to model the underlying process as it is. One differences the time series usually to get rid of periodicities or trends, but if that periodicity or trend is actually what you are trying to model, then differencing them might seem like a last resort option (or an option in order to model the residuals with a more complex stochastic process).
3. This really depends on the area you are working on. It could be a problem with the deterministic model also. However, depending on the form of the autocorrelation, it can be easily seen when the autocorrelation arises due to, e.g., flicker noise, ARMA-like noise or if it is a residual underlying periodic source (in which case you would maybe want to increase the number of fourier coefficients).