As asked, this is the code you would write to get the previous year's beginning:

    private static final MonthDay FIRST_DAY_OF_YEAR = new MonthDay(DateTimeConstants.SEPTEMBER, 1);

    public Date getPreviousYearBeginning() {
        LocalDate currentDate = LocalDate.now();
        LocalDate previousYear = currentDate;

        if (currentDate.isAfter(FIRST_DAY_OF_YEAR)){
            previousYear = previousYear.minusYears(1);
        }

        previousYear = previousYear.minusYears(1)
                .withDayOfMonth(FIRST_DAY_OF_YEAR.getDayOfMonth())
                .withMonthOfYear(FIRST_DAY_OF_YEAR.getMonthOfYear());

        return previousYear.toDate();
    }