Yes, they are an accurate summary of violent crime statistics.
Violent crime was rising by 10% from 2014 to 2016.. To be clear, that was for 1.5-2.5 years ago (in Trump's defense, the article he is - probably - citing - does not make that obvious if you go by the blurb, since the study results were published in 2018).
From AP article (in Chicago Tribune)
The recent influx of mostly young, male migrants into Germany has led to an increase in violent crime in the country, according to a government-funded study published Wednesday.
The study used figures from the northern state of Lower Saxony to examine the impact of refugee arrivals on crime in 2015 and 2016, a period when the number of violent crimes reported increased by 10.4 percent.
From January 2018 article "Violent crime rises in Germany and is attributed to refugees" carried by Reuters:
BERLIN (Reuters) - Young male refugees in Germany got the blame on Wednesday for most of a two-year increase in violent crime, adding fuel to the country’s political debate over migrants.
Violent crime rose by about 10 percent in 2015 and 2016, a study showed. It attributed more than 90 percent of that to young male refugees.
the referenced study cited by both AP and Reuters is available in German (PDF warning). There is little reason to doubt these news outlets have reported the findings accurately. Please note that the articles characterized the study as "government-sponsored", whatever that means in Germany's context.
From the study done by Pfeiffer, p 91:
At the end of the evaluations, we would like to return to the starting point. After seven years of continuous decline in violent crime, both in Lower Saxony and in Germany as a whole there was a significant increase in the number of violent crimes registered by the police for the first time during the two years 2015 and 2016. Using Lower Saxony as an example, we have shown that the new development is largely based on the immigration of refugees. For Germany as a whole, Federal Minister of the Interior de Maizière also confirmed this on the basis of the PKS data for 2016.
Accompanying footnote: Press conference of 24 April 2017 on PKS 2016, but the Federal Minister of the Interior used the term "immigrant" here because many federal states subsumed the refugees under this generic term.
It should be noted that the author of the study is highly respected in most circles and at the same time heavily criticised for his work and alleged biases in other circles. In this case the actual number of 10% is given for Lower Saxony and for the whole country this source just extrapolates and gives "a similar trend" but no actual number.
The number 10% is found on p71 of that study:
Tabelle 13: Anzahl aufgeklärte Fälle der Gewaltkriminalität mit tatverdächtigen Deutschen, Flüchtlingen und sonstigen Nichtdeutschen (Quelle: PKS Niedersachsen 2012-2016) [Number of solved cases of violent crime with suspected Germans, refugees and other non-Germans (Source: PKS Niedersachsen 2012-2016)]
- with German suspects: -0.9%
- with refugee suspects: +241.7 %
- with other non-German suspect: +10%
- total of solved cases: +11.4%
This is from the chapter: 5 refugees in Lower Saxony as victims and perpetrators of violence ––
5.1 The increase in violent crime in Lower Saxony since 2014 - is there a connection with the strong influx since 2015?"
And for overall registered cases of violent crimes the 10% pop up again::
After a seven-year period of decline, the number of violent crimes registered by the police in Lower Saxony has risen significantly again for the first time (+10.4%) in 2015 and 2016. A PKS data analysis carried out by the LKA Niedersachsen shows that 92.1% of this increase is attributable to refugees. Parallel to the large wave of refugees that began in September 2015, the number of cases solved with suspected asylum seekers increased 3.4-fold between 2014 and 2016. This can partly be explained by the fact that the number of refugees registered in Lower Saxony has more than doubled since 2014 (+117.0%).
This addition is just quoting the material from the study. It does not evaluate the study! Note also that "solved crimes" is not the same as committed crimes!
For even more perspective from the same study:
Comparing this with statistical data provided by the Federal Police of Germany (BKA) for the entire state gives the following numbers/diagrams:
But overall "crime" is summarized by the same institution as
Crime | No of cases 2016 | No of cases 2015 | change in %
total | 6.372.526 | 6.330.649 | +0.7%
law violations | 5.884.815 | 5.927.908 | -0,7%
violent crimes | 193.542 | 181.386 | +6.7%
One thing not done, but something that would have been useful, is comparing these crime rates, bot in their relational as well as absolute numbers with those statistics from the US!