Joda-Time library provides us a Virtual Clock utility named "DateTimeUtils". This is a demonstration for mocking start-end times.

StartEndTimeWithJodaTime.java

import org.joda.time.DateTime;

public class StartEndTimeWithJodaTime {

    private DateTime startTime;

    private DateTime endTime;

    public void process() {
        startTime = DateTime.now();

        // some heavy processing
        System.out.println("Processing...");

        endTime = DateTime.now();
    }

    public DateTime getStartTime() {
        return startTime;
    }

    public DateTime getEndTime() {
        return endTime;
    }

}

StartEndTimeWithJodaTimeTest.java

import org.joda.time.DateTime;
import org.joda.time.DateTimeUtils;
import org.junit.After;
import org.junit.Test;

import static org.hamcrest.Matchers.equalTo;
import static org.junit.Assert.assertThat;
import static org.mockito.Mockito.mock;
import static org.mockito.Mockito.when;

public class StartEndTimeWithJodaTimeTest {

    @Test
    public void saveStartEndTimeOfProcessing() {
        final DateTime now = new DateTime(1989, 7, 4, 1, 15);
        final DateTime fiveMinutesLater = now.plusMinutes(5);

        // We need mock millis provider, because we need to return different times for each DateTime.now() calls
        DateTimeUtils.MillisProvider mockMillisProvider = mock(DateTimeUtils.MillisProvider.class);
        when(mockMillisProvider.getMillis()).thenReturn(now.getMillis()).thenReturn(fiveMinutesLater.getMillis());
        DateTimeUtils.setCurrentMillisProvider(mockMillisProvider);

        StartEndTimeWithJodaTime processor = new StartEndTimeWithJodaTime();

        processor.process();

        assertThat(processor.getStartTime(), equalTo(now));
        assertThat(processor.getEndTime(), equalTo(fiveMinutesLater));
    }

    @After
    public void after() {
        // Use this to reset mock millis provider to system millis provider
        DateTimeUtils.setCurrentMillisSystem();
    }

}